In the middle ages, saints' relics were an important part of Christian devotion. Saints' leftover bits ranging from teeth to full bodies would preserve the saint's ability to do miracles long after his or her death. As you might expect, relics associated with Jesus himself were especially powerful and popular, but the problem was that he took all his bodily parts to heaven with Him and there was no possibility of body relics as with the saints. So the relics associated with Jesus were the fairly common fragments of the True Cross, countless nails from the crucifixion, as well as pieces of cloth associated with the passion, for example the so called Veronica that had the face of Jesus miraculously imprinted on it when it was used to wipe sweat from his face as he carried the cross. Jesus' foreskin from his circumcision was another relic associated with him, and one of the few possible bodily relics. So, yes, not only was Jesus circumcised, someone went to the trouble of preserving the leftover bits for over a millennium so that they could become medieval relics. Or at least that is what medieval people believed.

Presumably, yeah. Circumcision has always been a fairly universal among Jewish men. In Jesus' era that wasn't always true, it did occur that men would not circumcise their children or would reverse the process on themselves in order to be better integrated into Hellenistic society. This was the cause of some consternation in Jewish circles.

However, there is nothing to suggest Jesus or his family were part of that society, so the logical assumption is that he was circumcised.