Just in case anyone's wondering:
- I am rested <> Je suis reposé
- I rested <> Je me suis reposé
No. There are a series of action verbs which require ÊTRE instead of AVOIR for passé composé. They form an acronym MRS. VANDERTRAMP, or something along those lines, to remember which verbs those are. They include mourir, rester, tomber, aller, and some others. I'm sorry that I don't remember them all. If anyone wants to correct me or add more of these verbs, feel free to do so.
Monter -- monté (went up)
Retourner -- retourné (returned)
Sortir -- sorti (went out)
Venir -- venu (came)
Arriver -- arrivé (arrived)
Naître -- né (was born)
Descendre -- descendu (went down)
Entrer -- entré (entered)
Rester -- resté (stayed)
Tomber -- tombé (fell)
Rentrer -- rentré (went back in)
Aller -- allé (went)
Mourir -- mort (died)
Partir -- parti (left)
Here "y" would imply that you're talking about a specific place already mentioned, and would translate to: "I stayed there".
Because 'rester' is an être verb. Take a look here: http://french.about.com/od/grammar/a/etreverbs.htm
Because 'je reste' is 'I am resting', the present tense. The verb form used here is 'resté', which is the past participle, the equivalent of saying in English 'I have stayed'. The article 'to have' acts as an auxiliary to the participle, as it very often does in French. However, in the case of a few exceptions, the auxiliary is not 'avoir', but 'être', and 'rester' is one of these exceptions. Therfore:
Je reste - I am staying Je suis resté - I stayed
Please read the earlier comments, someone said that they tried it and it was accepted as correct.