Proof I own ERC20 tokens without giving my wallet address - possible?

I'm looking for some code/tools that can help me with the following use cases, the last one being the hardest, using my ethereum account/key. For some I have found something, but for others not and I certainly haven't "one tool to rule them all":

1. Proof that I control/own a certain eth-address -> I can do simply that using MEW sign message & verify message
2. Someone wants to send me a message that only I should be able to read. So the input on their end is my eth-address (as that's kind of my public key) & the message, the output some kind of string. I should then be able to decipher it with my private key. The only thing I found is some code here: https://ethvigil.com/docs/eth_sign_example_code/ , does anyone have a better tool/idea?
3. And the hardest - I have some NMR ERC-20 tokens in my wallet ( https://etherscan.io/token/0x1776e1F26f98b1A5dF9cD347953a26dd3Cb46671 ). I do want to prove to someone that I have NMR tokens, but I don't want them to know how many exactly (which also implies that I can't give them my wallet address). Is there any way I can achieve that (preferably a tool/some code)? Sounds a bit like "zero-evidence-proof" to me :-).

Thanks for any insights!