What is the easiest and fastest way to check their balance?
I'm going to ignore the "fastest" and answer the "easiest" question: install Bitcoin Core, load all wallets, then let it sync. Depending on your hardware this may take a day (or longer). Once done, check the balances.
Also, is there any way to check whether this dust (if available) also generated some $ on forks like Bitcoin Cash?
There's a website for this, but it's not always reliable. The best way is to export your addresses and check them on a block explorer. Or import them into a Forked wallet, but know that you shouldn't trust them. So use a VM or take other measures to protect your system from malware.