Learn Italian: La ragazza è talmente sbadata che ha urtato la porta. - The girl is so careless that she bumped into the door.

Yes, absolutely. Talmente ... che and così ... che both mean "so ... that" and are completely interchangeable. Saying così sbadata che would mean exactly the same thing.

Why is ha urtato in the indicative mood rather than the subjunctive?

Clauses introduced by talmente ... che describe a real, factual result (she actually bumped into the door). Because you are stating a fact, you use the indicative mood (ha urtato). The subjunctive is only used in consecutive clauses if the result is hypothetical or just a desired goal.

Does the verb urtare (to bump into) require a preposition here?

Not in this sentence. Here, urtare is used as a transitive verb, meaning it connects directly to its object without a preposition. You just say ha urtato la porta (she bumped the door) rather than using a word for "into". While you can sometimes say urtare contro, the direct approach used here is very common and natural.

Could I use the imperfect tense (urtava) instead of the passato prossimo (ha urtato)?

No, because bumping into the door was a single, sudden, and completed action. The talmente ... che structure here shows the immediate result of her carelessness in that specific moment, so the passato prossimo (ha urtato) is the correct choice.