Your coins should be safe as long as you don't do something careless like expose your wallet's private keys one way or another.

I really don't know the technical specifics, but one of the main differences with ETH 1.0 and 2.0 is that 2.0 will move into proof of stake, meaning people wouldn't be able to mine ETH the way people mine Bitcoin. Instead of buying GPU hardware, they "stake" their ETH instead, locking them up for a certain timespan.