Dear Mr. C:

You wrote:

Which among the sentences below is or are correct?

1. Marvin plays basketball well as I do.
2. Marvin plays basketball well like I do.
3. Marvin plays basketball as well as I do.

As they stand, only #3 is grammatically correct, though you do hear people say #2.

#1 would be correct with a comma after well, marking the division between the two separate clauses. That would say something different from #3.

#3 says that Marvin plays with the same ability that I play with. There is a comparison.

“Marvin plays basketball well, as I do” simply says that both Marvin and I play well, but with no comparison implied.

In standard written English, like is a preposition, not a conjunction, so #2 is nonstandard since like is followed by a clause.

I hope this helps.