He sounds completely normal to me. I think it's the preschool that might be a bad fit. My son still sometimes cries when we drop him at school, and he's been going over a year (new school starting this past August). His teachers and the preschool owner don't seem bothered by it at all. They take him to play or feed the fish or distract him in some way, then he's fine and has a fun day. One of our friends told us their younger daughter cried every day they dropped her at school until she was in 1st grade (a now perfectly adjusted 16 year old)! When I've asked my son why he's crying, it's just that he'd rather be with us then going away from us for the day.
As for the playing with other kids, I think that's normal too. At 3, kids start moving away from parallel play and into interaction, but not every minute. Plus he's new to the school and, therefore, the kids, and only goes twice a week. My son still sometimes doesn't play with, only near, the kids. Even last night, with one of his best friends, they were playing like crazy, then we heard silence. We went in to check and they were sitting near each other playing with different things. Totally normal.
You may want to consider another school if this teacher doesn't understand this. Also, with 16 kids, there should be 1 teacher plus 2 aides. If not, the kids aren't getting enough supervision and help to socialize, IMHO.