This is a bunch of questions, so I will give only a short answer to each.
If you want more details, please ask a follow-up question with a narrower focus to dig deeper.
What are the superlative and comparative forms of "optimus"?
There are none, as optimus is a superlative already.
It is not unique in that respect; pessimus, maximus, and minimus behave similarly.
You could always form *optimior and *optimissimus, but as far as I know they have never been used.
And even if you can find an attestation (I couldn't in a classical text corpus), such forms are certainly not a part of standard Latin of any era.
Why is it also used as a simple adjective, meaning simply "excellent" and not a comparative?
Latin superlatives are often used absolutely, without comparison.
Just like optimus can mean "best" or "very good", the regular altissimus can mean "tallest" or "very tall".
English doesn't do this to the same extent, so it is often most natural to translate a superlative using "very" or some other form of emphasis.
Optimus is not special in this respect.
Isn't "optimus" a suppletive comparative for "bonus"?
It is the suppletive superlative of bonus.
The comparative would be melior.
All degrees of comparison look different.
What are the differences in Latin in the use of the superlative, comparative and normal adjectives? I read that Latin was more flexible than English. What does it mean concretely?
Without more context, it's hard to tell what was meant; I can't give a more concrete answer without a more concrete question.
I suppose it meant that comparative and superlative forms in Latin do not always imply comparison.
This is rarer with the comparative than the superlative.