Learn Italian: Il motore è arrugginito, quindi lo inizio a pulire. - The engine is rusty, so I am starting to clean it.

With aspectual verbs like iniziare a (to start to) or finire di (to finish), you have two choices for pronoun placement. You can attach the pronoun to the end of the infinitive (inizio a pulirlo) or pull it in front of the conjugated verb (lo inizio a pulire). Both are perfectly correct, but this front placement (called clitic climbing) is very common in spoken Italian.

Does the preposition a affect how the pronoun moves?

Not at all. Aspectual verbs that require a preposition like a or di before the infinitive still allow the pronoun to jump to the front. You simply leave the preposition exactly where it usually goes, sandwiched between the conjugated verb and the infinitive.

If I changed the second half of the sentence to the past tense, would the participle change?

Yes, if you move the pronoun to the front! In the passato prossimo, if the direct object pronoun climbs to the front, the past participle of the first verb must agree with it. Since motore is masculine singular, you would say l'ho iniziato a pulire. If you left the pronoun at the end of the infinitive, there is no agreement: ho iniziato a pulirlo.

Is arrugginito acting as a verb or an adjective here?