Gemma I think he sounds perfectly normal - 'sometimes hits and has tantrums' - that is ALL children!!! Also, with the biting, I know the nursery have said they have not had it go on so long before, but I really wouldn't worry. ALL children do things differently and learn at different times, and he's very very young, only just two. He's only just learning that things he does have an effect and he's not old enough to realise when things hurt others. NSPCC advice states that under two, children can't be deliberately naughty, because they act on the impulse of the moment basically.
Other people are always ready with their opinions, ie, on the biting going on for a long time, but remember it's just an opinion.
You say that he plays very well with others usually, so I'm sure he's just a normal little boy. He obviously likes routine alot and order, and alot of toddlers are like this, my son isn't so obsessed with tidiness but I do find he and lots of toddlers get very very bossy and want things done in the same way every time. my son still moves a picture back to where it was about a year ago, when he visits a friends house, because that's where he first saw it!
I really wouldn't worry, just keep an eye on the obsessiveness and seek help from GP if ever you feel it's stopping him from doing things he wants to do. One thing I have learned as a mum, probably the MAIN thing, is ACCEPT THEM! They are all different, in some ways all bizarre and quite loopy, and we save ourselves loads of worry if we simply accept them and their foibles. Basically if he's doing it, it's normal for him! It's only if it hurts him or others, or hinders his development in some way, that it's a problem. Enjoy your lovely boy.