- Yes - through GPS in the bitcoin wallet code can be correct if you are using some unknown wallet that may have a backdoor
not that there is any that i have seen so far!
I haven't seen GPS in wallet code yet. Of course it would have to have GPS hardware to operate as well. Theoretically possible on a phone wallet.

- Yes - your identity is always revealed this depends on the type of wallet you are using. if you are using a WALLET like bitcoin core, armory, electrum,... then it is not. but if you are using a bitcoin ACCOUNT which they call wallet such as coinbase then it is true.
The key word in this answer would be "always". Rather than "in some cases".
- Yes - through the nodes this can also be true but not easy. basically you have to create a ton of nodes and connect to a ton of other nodes. then you select someone's node and connect to it and fill all its connection slots. each time that node sends a transaction you check to see whether you have seen this transaction before (if it is relaying it) or it is a new one (creating it). if it is new then he owns the coins.
> Can nodes tell which bitcoin addresses belong to which IP addresses?
No.