l’L'adaptation cinématographique

Il y a quelques jours, j’ai regardé la nouvelle série (télé de) « Percy Jackson ».

It would be better to directly quote the title IMO because a totally uninformed reader could believe that "Percy Jackson" is the author's name
You're not forced to add "télé", given the context, although doing it isn't wrong of course

Je trouve/pense que cette série est un exemple d’une adaptation cinématographique qui marche bienréussie.

"trouve" is especially good if your opinion is a feeling/impression more than a mental analysis
"qui marche bien" could have different meanings (for example, an adaptation that makes lots of money)
"réussie" clearly indicates you mean it's well done

Les livres dea saga « Percy Jackson son» est très connuse et cette série permet aux fans de regarder l’histoire prendre vie à l’écran.

Une saga = a series of book (in the literal sense, it's about Norse sagas of course)

Les films de Percy Jackson ne sont pas de bonnes adaptations parce qu’ils ont trop changé l'histoire.

You're not forced to repeat "Percy Jackson" now we know what you're talking about

Cependant, lcertaines adaptations comme How to Train Your« Dragons », qui ne [suit/suivent ?] pas du tout l’intrigue originale peuve, [sont également marcher.correctes ?]

It's just called "Dragons" in French
"qui ne suit pas" would mean only "Dragons" doesn't follow the original story; "qui ne suivent" (agreement with "adaptations") would mean all adaptations of this sort don't follow their original stories. I don't know which one you meant
I suppose you meant these adaptions are also alright, in which case, you can phrase it as above

Avez-vous lu les livres de« Percy Jackson » ?