Verbal adjectives

Hey!
I'm new here so please forgive me if I do anything wrong.
My question is about adjectives. Verbal adjectives.
I'm using an app called "drops: learn Japanese" and in the section "emotions" there is a bunch of adjectives that aren't really い adjectives or な adjectives. I thought that maybe they are verbal adjectives but they don't really follow the pattern for verbs as well.
There are adjectives such as: やすまった、ほれている、くつるいだ.
For い and な adjectives we add くない or じゃない to make a negative form. How to change these words into negative forms.

Those are not adjectives but conjugation forms of verbs, "the past form of やすまる", "the -te form of ほれる ＋ auxiliary verb いる" and "the past form of くつろぐ (You misread the third one. It's actually くつろいだ.)", respectively.

Hey thank you so much
So it's something like write - written (eg written language; used as an adjective).
But how do I know when to add いる and when to follow basic verb conjugation.

It's more likely modifying clause (corresponding to relative clause in English grammar) even just for a single word. Thus, the construction is closer to "language that is written" than "written language", therefore it can have tense, aspect or mood.
e.g.
書かれた言語
language that is written

書きたくない言語
language that I don't want to write

書けなかった言語
language that I was not able to write

いる is used there because the -te iru form expresses an aspect of the verb (the present state resulting from the past action in this case), not because to connect ほれて to a noun. First, the form is chosen to express the meaning, and then it's used to modify the following noun.