Lol, I hoped i'd never have to explain this...it's complicated.
There WAS magic before Spyder, and there WAS a Weave before Spyder. BUT, the magic that existed before Spyder was the same as you'd find in other prime material planes. Stronger, yes. With more potential, yes. With many many more people able to use it, yes. But there was a "glass ceiling" that limited just how much power could be brought to bear. The Weave was the hammer that broke this glass ceiling.
The Weave was created with the first four sentient races; elves, humans, dwarves, and goblins. It was tied to them in such a way that the power of magic would always depend on the population of those who could use it...the Sorcerers. But there was no sui'kun at first, because:
THE SENTIENT RACES WERE NOT YET READY TO HAVE THE RESPONSIBILITY OF USING THAT POWER.
Remember, they started as cavemen...would you REALLY want to put that kind of raw magical power in the hands of a caveman?
Niami, and the other Elder Gods for that matter, thought it best to let the sentient races mature, to develop, before handing them that particular Pandora's Box.
After a few dozen millenia, after civilization had taken hold and the basic level of intelligence of at least 3 of those 4 races had reached what the gods felt was a reasonable level, Niami began setting into motion the events that would lead to the first sui'kun...Spyder.
Spyder was the first Sui'Kun. Spyder represents Sennadar's magical power...literally. When she was born, the laws of magic on Sennadar were changed, breaking the glass ceiling and making it possible for magicians of all 4 orders to reach into magic that had, to that point, been denied to them. Just as the birth of each new sui'kun during the Firestaff series raised the level of magic that could be used, Spyder represents that core threshold that separates Sennadar from other material planes.
And yes, the Weave can exist without sui'kun, so long as there were Sorcerers alive to preserve it. But without sui'kun, the Weave has very little power.
If some miraculous disaster happened and all the sui'kun died, then the Weave WOULD be destroyed. It wouldn't be able to survive that kind of trauma. But Niami could rebuild it, as long as there were Sorcerers alive to serve as the heart that caused the power to flow through the strands. This new Weave wouldn't be able to sustain any kind of significant magic, for a VERY long time, until it was strong enough to do so and a new sui'kun was born to take on the burden of being the prime focus.
But Niami could rebuild it. It would take a very, very long time, but it could be done.
As to the age of Sennadar:
Hate to shock ya, but Sennadar is MUCH YOUNGER than most other Primes. The primes closest to the Core are the NEWEST planes. Remember my references to those "true ancients" WAY back in book 1 of the Firestaff series, and those cities that legend said were falling into ruin long before humans moved out of caves? They weren't the Sha'Kar, and they weren't the First Races either. They were from another plane, and they vanished because the Elder Gods wiped them out. They were from a much older plane...or it had been up until that point.
They came to Sennadar because their own plane was destroyed. Those refugees that came to Sennadar were also wiped out, because of two reasons; they were contaminating the progress of the natives and disrupting the intent of the Elder Gods for the plane (they were much more advanced), and they brought something with them that the Elder Gods did NOT want on Sennadar.
Sennadar's recorded history goes back about 20,000 years. Pre-recorded history goes back about 50,000 years more.