I found a few sentences (which, I'm pretty sure, should be correct).

Féach chomh scamallach is atá sé.
Féach chomh deas is atá mo chuid gruaige.
Féach chomh fada is atá sí freisin.
Féach chomh fada is a bhí tú á ní.
Féach chomh gnóthach is atáim, á dhéanamh duit.

Now, the part that I'm interested in, is is atá/bhí/... sé/sí/... What is the purpose of is there in grammatical terms (I don't know even what to look for in grammar books) and would it be possible to say it without is (Féach chomh scamallach atá sé, etc, as I would do automatically)?

is = agus = and
Here it is used in the sense of English "as"

chomh ... agus ... = as ... as ... (followed by a relative clause)

chomh scamallach is atá sé = as cloudy as it is = how cloudy it is

Féach chomh scamallach is atá sé. = Look, how cloudy it is.

is/agus is necessary when a relative clause follows.
In case there’s only a noun you’d use le:

chomh scamallach le lá geimhridh = as cloudy as a winter’s day

So simple... Thank you, as well as pointing out the case of le with a noun.