Learn English – Can you explain the meaning of this sentence

It means the same as it normally means. In the phrase "couldn't be more" optimistic, it means that he is as optimistic as he could possibly be - that they will do well. He couldn't expect that they will do well any more than he already does.

You can't have "strong feeling" in this way, because feeling here is an ordinary noun. You must have a feeling or plural feelings. Fortunately, strong feelings is a set phrase.

An idiomatic conversation might be:

What do you think? Is it beautiful or not?
I don't have strong feelings one way or the other.

Note the omission of the last "beautiful". It's implied in the not; you don't need to repeat it.

The respondent uses the set phrase "strong feelings". The feelings need to be qualified in some way, and "one way or the other" is a set phrase which refers to the two alternatives offered. You could say "I don't have strong feelings about it."

Note that having feelings for normally refers to some sort of affection. If you have feelings for someone, you are attracted to them. Having feelings for some thing might be misinterpreted. If the conversation was about a sheep, for example (a sheep might have a particularly beatific facial expression), you don't want to say you have feelings for it!