your title and your poll are asking two different questions though. finding out whether someone has bitcoin or not can be a little different than finding how much and which coins.
for example when someone talks about bitcoin all the time, visits bitcoin related websites (bitcointalk, coinbase,...), has a bitcoin wallet installed then it is a safe assumption that they own bitcoin.
but knowing which address belongs to you and how much bitcoin you own is a much harder thing.

in any case multiple choices of that poll can be correct.

• Yes - it is pseudo anonymous so if you are not careful it can be revealed is the most obvious answer.
  
• 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!
  
• 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.
  
• 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.