Thank you for the reply. Is it possible to install Electrum (not ElectrumX, just standard one) on server and access it commands?
Yes, of course.
ElectrumX is an electrum server (Clients (standard electrum) contacts electrum servers to get the block header and all necessary information).
You don't need to (and according to your post: don't want to) run an electrum server.
Note that running electrum on a server is NOT the same as running an electrum server.
Simply install electrum on your server.
I also saw Electrum for LTC and DASH for example. Looks like they all share the same Python command interface. Does that mean that they are also capable to do the same things as Electrum BTC does?
The official electrum only supports BTC. All other versions for other coins are forks.
IF they support the same commands, then yes.. they can do the same as the original electrum. But you'll have to check that first.