Smaoiníos go téann dobhriathair tar éis na focail uile eile, ach tá abairtí mar "Teastaíonn uaim rud éigin," a dtéann an réamhfhocail tar éis an briathar díreach ann

Mar sin, cad a téann dobhraithair agus réamhfhocail in abairtí?

(Tá brón orm go leor as mo Gaeilinn dona Le do thoil, ceartaigh mé an teastaíonn uait )

Your sentence is not correct or something is missing.

Correct is:
Teastaíonn rud éigin uaim. = I want/need something.
In sentences with normal nouns as (grammatical) subject (here: rud éigin), the subject is in normal position following the verb.

But ...
Teastaíonn uaim ... occurs in case of verbal nouns ("infinitives"):
Teastaíonn uaim labhairt leat. = I want to talk to you.
Teastaíonn uaim dul abhaile. = I want to go home.
Teastaíonn uaim rud éigin a dhéanamh. = I want to do something.
or in case of dependent clauses (go):
Teastaíonn uaim go ndéanfaidh tú rud éigin. = I want that you’ll do something.

Such subjects are considered "complex" and so they are put at the end of a sentence.
(even in cases of single verbal nouns, e.g. Teastaíonn uaim codladh. = I want to sleep.)

It's very difficult to understand what you are trying to say in Irish.

Smaoiníos: = do smaoiníos (the "do" is needed with a non-lenitable initial consonant). This verb means "to reflect, consider".
I thought = do shíleas, or "is é do shíleas ná go..."
Go dtéann: Go takes eclipsis
Tar éis: takes the genitive
Uile eile: I've never seen "uile eile" before. Tar éis gach focal eile?
Preposition in the singular = réamhfhocal
Cad a téann: cad means "what?" and "a" would take lenition or eclipsis depending on the syntax. Where does it go? Cá háit go dtéann sé?
Uaim: is not a preposition. It's a prepositional pronoun.

Teastaíonn uaim rud éigin: teastaíonn (is needed) uaim (from me) rud éigin (something): I need something, expressed impersonally as something is lacking from me.

"Is é do shíleas ná go dtéann na do-bhriathair tar éis gach focal eile, ach tá abairtí ann, mar "teastaíonn uaim rud éigin", agus is go díreach tar éis an bhriathair a théann an réamh-fhocal iontu. Cá háit is ceart go dtéann/go raghadh na do-bhriathair agus na réamh-fhocail san abairt?" [I'm open to corrections, but something like this.]

Yes I'm so sorry!

I've just been learning for a few weeks and I figured I'd at least try, and maybe it'd be close to comprehendible but apparently not lmfao

Tysm for taking the time to correct me!