But I'm confused, what about getting private key of certain address. Imagine I have used z address, will I be able to get private key for that address?
Yes, You should be able to get your private keys from ZecWallet full-node and ZecWallet lite. Alternative clients seems not to support shielded-address option.
Besides, can you suggest me other wallet for zcash which can be compared with Electrum for bitcoin?
I found
this announcement made a year ago about working on the developement of electrum-zcash but no further info.
Try this one called electrumx which is also still under developement and support other altcoins too (Electrum version for alts):
https://electrumx.readthedocs.io/en/latest/