1) The purpose of the receive tab is explained
here. It's just to provide a workflow for receiving bitcoin. If you prefer to use the addresses tab instead then that is ok too.
2) Disable full wallet file encryption if opening electrum is too cumbersome for you. That is go to wallet menu > password enter your password in all three fields and uncheck encrypt wallet file at the bottom. If you do it like this you will still need the password to spend your bitcoins but not to view your wallet file and get receiving addresses.
Otherwise do as xdrpx said. That command can also be run on the command line `electrum listaddresses` on linux and MacOSx.
3) Addresses are generated in sequence and behind the scenes each address has an index number like 0,1,2 etc. Electrum considers an address as "used" if it has received bitcoin to it at least once. Electrum maintains 20 unused addresses past the index of the last used address. That number 20 is the default gap limit or lookahead window. So the answer to your question is that as you start to receive funds to your addresses Electrum will generate new ones automatically.
Note that if you change the gap limit like xdrpx said you better make sure to note it down alongside your seed backup so that if, in future, you restore your Electrum wallet you can change the gap limit again. You will have to do that if you restore from seed.