I received miner reward even though I haven't leased my coins. Do the coins automatically lease?
Did you receive MRT or WCT? The only way to receive MRT distributions is to stake.
MRT. I'm aware what WCT is.
I haven't been staking as far as I know. I just leave my coins in my wallet
That's a good question then! I dunno how you'd get MRT. :/
Trying to lease, but getting the following error. Have tried 2 different leasing addresses and differing amounts. Anyone know why? Running most recent Lite client, version 0.4.18a.
email support@wavesplatform.com for that one.
When I lease my Waves with the new wallet, will I still get WBTC rewards (from Byteball sales) and other airdropped assets? Or will the receiver of the lease get those assets?
Yes you get the airdrops. When you lease, you still own the waves and the waves are still in your wallet. Any airdrops allocated to waves holders still go to the holders.
Do I need the lite wallet running in order to lease 
Nope! You just need to lease the tokens and that's it. Just keep in mind that it takes 1000 blocks (about 16 hours and a bit) for the lease to take effect, and 1000 blocks for the lease to cancel if you ever want to stop leasing your waves.