Hey this is my take on the questions, it could be wrong. I just like to play around with ideas. Don't take any of my answers as cannon, it's just speculation/postulation.
If a real powerfull priest can open a gate to Astral and Tarrin needs his full power to do it, does it mean Tarrin (as is) is less powerful than a powerful priest, who only get to use a part of his/her patron-gods power?
Miranda is more powerful than mearly a real powerful priest. She is the living icon of her goddess, she has a special link with her goddess and who knows what stuff that allows.
What I'm asking is this: Is Tarrin wrong in presuming his equality in a fight with a younger god? I mean, if Tarrin is less powerful than the powerful priest, does it mean that the power a god can call upon the material plane less than that of a powerful priest, or is Tarrin wrong?
He's also presuming that when fighting a younger god, his sword would turn him into a god who doesn't know how to use his power fully. Like the battle against Val, and when in that state, he can open up portals like Fel said.
If a god is spread out over many dimensions (thats why they can't call upon all their power in the material plane, right?(Btw, is the soul also on the material plane?)), how does those dimensions fit into all the world-dimension. Are all those god-dimesions part of the world-dimensions or do they streach into another axis?
The way I see it, there are multiple dimensions beyond 3/4 in a reality. And then there are multiple realities. The gods reside in all the dimensions in one reality, but a god usually stays in one reality, unless there is a copy of him in another. This is totally based on my belief/opinion. Very minimal support for this one from just the books.
What andout the soul then? If its not part of the material dimension, is it then on one of the god-dimensions (If it is, why couldn't then Val attack Tarrin on this dimension?), or has it got its own spirit-dimensions in yet another axis of reaily? If the souls got an own spirit-dimension, how can then the gods of death get to them?
I think the soul reside on the same dimension/reality as the physical body. Usually within the body. When a soul is freed from the body, it is still in the material plane. Hence no need for the spirit dimension/the other questions you posed

... Of course this could totally not fit with what Fel is planning, so it's a pending answer.
Is that why gods' souls are destroyd when thay die, because they're not part of the spirit-dimension?
This answer is built upon the Xanth series idea but different. Gods are souls. When a soul is destroyed it gets dissipated and dispersed, unless you got a soul trap ready to suck up all those peices and contain them. After time, the pieces would coalesce once again to form the soul. The god's physical being is totally manifested through the icon which is built by the power of the god over time.
Hence why gods needs the icon, and without it they don't have a connection to the material world. Hence why Miranda has all her preistly powers in another reality, she is a living icon. So if Miranda's god has followers in the reality Miranda is in, the priests there would probably have the same powers as the priests in Sennadar.
In summoning the spirit of an elemental, isn't that breaking the dimensional barrier, with relatively little power? Or is it the spirit-dimension here also, that you can go thru it?
If it's so low power, you try summoning a spirit of an elemental! Lol, I always thought it was a high power spell. And plus it's a non-physical portal, just the spirit needs to get through. Since it takes a lot more energy to bring matter across a reality barrier than energy. And spirits are mostly comprised of energy. :-D
But why can't the spirits The One caught go to the spirit-dimension then?
What spirit dimension? The spirits are trapped in the material plane. I wonder if Pandelbrass has enough power to breach a God's blockade.
What about demons and otherwordly weapons? Is it because when they enter another world-dimension (or is this just sennadar and pyrosia?) they get spread out on some god-dimensions also?
Maybe Fel had meant the demon dimension? Like wood from Pyroasia can't harm the demon still because the wood isn't from the demon dimension. Before Tarrin only know about Sennadar, and other dimension. And just thought all other dimensions were the same, and didn't know the items had to come specifically from the demon dimension to harm the demons? Like krypton fragments can hurt superman, pieces of Pluto won't do diddly to Superman, but in a sense you can call krypton pieces, other-worldly rock. And only other-worldly rock can hurt superman.
And is that why priest-magic can harm them, because it is also in part from thet god-dimension? If that is the case, then why doesn't somebody who leavs his/her world-dimension and return get spread out on many dimensions?
Eh? sounds like you already got a little dimensional system setup and this question pertains to that specifically. I wouldn't know the answer to this because I'm no expert on your system.. I'm just an expert on my system. hehe.
What about Tarrin & Co. (or just Tarrin) in Pyrosia? Can only otherwordly weapons harm them? And if not, why? Or if there is another reason to the demons invureability, what is it?
Answered previously. They are normal, they don't have demon like attributes because they aren't demons from the demon dimension.
The Weave. If it is thru the weave the gods grant their priests magick does that mean that the weave connects the god-dimensions with the material-dimension? And if that is so does that mean Niami has a different powerallocation than the other gods?
Gods can use weavespinner magic. Gods icon is in the material plane. When mortals ask for something to be done, the Gods through their icon, long distance cast certain spells. Hence the difference with priest/sorcerer magic. The long distance casting restricts it to certain types of spells, so the gods have to do a whole other set of spells which sorcerers don't use. Since sorcerers can't cast long distancely, don't have enough power to do so, and why would they want to change something half way around the world which they probably don't know about? So if Niami cuts out the weave, none of the gods can give the priests their magics because that support is gone. Godly or not, Gods would have to make personal appereances to do godly magic to supplement the unworking priestly ones. And no god would do that, their icon's are suceptable to getting destroyed.
If Niami removes the weave from the other gods is it then removed from the material-dimension also? If it isn't can't then the gods give power to their priests thru the material plane? And if Niami removes the weave, what happens t Miranda power? Or can she accsess her power thru her special link to Kikkali?
All of the weave would be gone, no magic, like the earth you are on now. No sorcerers can spin anything. Maybe even the were creatures would become weaker and weaker. Definately not as strong as before since it seems like the weave does improve the connection between the all and the druid/werecreatures. From the stronger sorcerer/stronger druid thing that happened to tarrin when he got re-turned.
Why does smaller priest spells from younger gods work in other worlds if the weave isn't there? Or is it? But that would mean that Tarrin should be able to do priestmagick in Pyrosia, or?
I thought Tarrin could do very simple preist magic like any other priest, but the magic is so simple it probably wouldn't have been helpful. Maybe magic like the priests on earth could do, make holy water, bless people, damn devils, psychosomatic healings.
What about wizards magic? It comes from another dimension into Sennadra even though Sennadar is blocked? Does it come thru the gate to the Astral och maybe the spirit-dimension?
Magic is energy, it can freely traverse realities, unless an entity is actively blocking that. The spirits would have come home, except it was blocked. Just like how the elemental spirits come through, as long as they have a guiding beacon like thing. Otherwise they wouldn't know how to get there. Travelling through realities is dangerous and risky. And it is very easy to get lost. So when a wizard calls forth his/her magic, it simply pulls the magic from whatever dimension the wizard magic comes from. If everything was blocked from comming into sennadar, then the gate that spyder guards would not have been possible. I think it is just incomming matter that is blocked/restricted to spyder's gate. And the gods probably aren't afriad of unwanted energy entities, since the gods can easily handle that without harming the physical plane of sennadar.
Lol, now someone is gonna have to read my answers and say that I'm all wrong. Atleast until Fel tells us exactly how the worlds works in his story. Maybe pyroasia is just another planet in another star system. Doesn't even have to be another reality. Perhaps that Sennadar is closest to the center of the galaxy where there is something special? Who knows. That would be simpler as a model to explain with.
- /= orbidder