て preceding 綺麗事 is the て-form of the auxiliary verb
いる. Dropping the
ている is very common in colloquial speech, I.E.
思ってる. This just gets slightly more confusing with sequential て-forms. You might think of it like this:
思う ー＞ 思っている ー＞ 思っていて。。。 ー＞ 思ってて。。。
In this case the second
て is just there to let the person continue their sentence. So for the sentence below
A very, very direct translation might look something like this:
(They) think it will be fine if they cry and are all superficial positivity, which makes (me) angry.
イライラする, it's certainly a mimetic.
mimetic+する is a sufficiently common pattern that I don't think if I would call this a "verb based on a mimetic" as much as just a normal mimetic; the
する here just describes the action of being in the state associated with the mimetic.
Edit: Please note my original interpretation of the sentence was incorrect as I misinterpreted the omitted subject for
思う. I'm using naruto's provided translation here
The protagonist thinks weeping solves everything and just talks about ideals, which pisses me off.