"At" indicates that he was present at the location of the accident; you woulnt say you were "at" an accident, but rather at the scene of the accident. "In" indicates that he was involved in the accident.
So let's say that John was driving a car and another car drove into his. You'd say:
John was in an accident.
If he was hurt, your say:
John was hurt in the accident.
In a different scenario, John is not a part of the accident, but happens to be at the location it occurred. You might say:
John is at the scene of the accident.
If he got hurt, you similarly use "at:"
John twisted his ankle while at the accident scene.
The reason behind the distinction between "accident" and its location, is that the accident has no inherent location. Obviously it happens somewhere, but when talking about "the acciden," you're talking about the occurrence and not the location. This is also found when you talk about the crash scene/site, crime scene, etc.
Both positions of "still" are acceptable, but after the verb ("He is still a boy") is much more common. (GloWbE has 86000 instances of "still + [be]" against 520000 instances of "[be] + still" (where by [be] I mean any part of the verb 'be' - am, is, are, were, being, etc.)
In Modern English, "yet" is almost confined to negative and interrogative contexts (it is a negative polarity item), so both of those sentences with 'yet' look old fashioned or poetical. I think the choice between them would be governed by prosody and rhythm rather than meaning.
Best Answer
The first sentence, "had my car cleaned," implies that someone else did it. "I had my car cleaned [by someone]." Disregarding tenses, you could say "my car was cleaned." The "had [something done]" setup typically implies that you instructed someone to do it.
The second sentence means that you cleaned it. Disregarding tenses again, you could say "I cleaned my car."