Electrum wallet can generate native segwit addresses (Bech32)
If you want for mobile then Samourai wallet can do that also.
Not so sure about the Electrum part as I'm still not getting this, but all I can see is that, addresses are getting changed back to back whenever I get out of the app and get back in. If it will be like this, how will I be able to receive coins over a single address only? Why can't we see a private key instead, so that we might just put it in some compatible wallet and start using it?
With electrum you keep the same addresses. Once you start the software, it will ask you if you want a legacy wallet or a segwit address, and then you get a wallet file, and this file will give you access to your coins, much like Bitcoin Core's wallet.dat, and also you will get a seed which can generate the content of this file anywhere you are at without holding the file (so save it somewhere that nobody can see it or better memorize them and destroy it).