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Basic BTC 101 question. Are there a fixed number of txns in a block or is it variable?

(And what do you recommend I read to learn this kind of stuff)

It's variable. Each miner decides (in software) which transactions to include in a block.

Everything is in here: https://en.bitcoin.it/wiki/Protocol_specification

Or read the source code for the standard client: https://github.com/bitcoin/bitcoin/blob/master/src/main.cpp

As far as I know there is no limit on the number of transactions, but there is a limit on the total number of possible bitcoins (about 21 million IIRC)

So when a node picks up a block to process it gathers up all of the pending transactions at that time?

Yes. (More like the node creates a block containing all pending transactions, but that's a nit.)

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