Is arbitrage a good idea in immature markets like crypto?

Actually, it is an opportunity in immature markets like crypto. You do need a lot of capital, program trading (aka bot) and predictable patterns. The last one is the difficult one. Many moons ago I worked on arbitraging 2 Brazilian stock exchanges which were carrying the same securities (3rd world issue). As for Brazil, back then it was legal...

Is arbitrum legit?

As you said, Arbitrum is legit, it works and its growing fast. What did you do with the half you sold? Holding it in stablecoins, not sure what to do yet but will probably buy the next dip with it. Honestly? I don't think it's the worst. I do like some of the function they have already. Cheap fees and a nice bridge function are good for usage.

Should I buy crypto / ETH?

Most crypto should be a long term play The dips from people unloading the airdrop may be a good buy opportunity. But you are also just risking a gamble on alts. Still stick to your btc / eth play and if you want to dabble in alts, allocate a small percent