When I restore wallet with my seed I get 0 bitcoins on it. I'm trying to find out what is wrong but I don't understand few things.
I can see that address starting with 15TR still has some coins and only one transaction from 2017, so your issue could be one of several things.
Either you didn't wait until wallet is synced or you used different seed words that are not generating same address.
how can I confirm that restored wallet is the correct one that received transaction on the link above?
Anyone, including me, can confirm that with any blockchain explorer from transaction link you posted.
What address you used and how you generated it is totally different question and only you can answer this.
is the seed case sensitive? my noted seed has got 12 words all lowercase only one word I have written down is with first letter capital. Does it matter? When I'm recovering wallet in electrum it does let me to restore wallet when I change letter to capital or lowercase but if I change the letter to different one it does not allow me to continue. Seems like it is case insensitive?
What wallet you exactly used for generating seed words?
Most seed words are lowercase, including most used BIP39, except if people are using some custom words that only complicates thing and I don't recommend doing that.
I don't think this is the problem in your case.
if I get my wallet restored correctly, how do I verify that someone hasn't got hold of my wallet and didn't transfer bitcoin out of my wallet? If the restored wallet is the one I expect would I see the transaction history in electrum with all transfers in and out?
If coins are still on your address (check with blockchair or other explorer) that probably means that nobody stole them from you.
Don't complicate things by asking so many questions, and first answer what was asked from you.