First of all don't panic. You have had him a few days and all the excitable jumping and bounding is just him being grateful and showing off, most probably. In a way it is better that he is like this, rather than scared and moping.
I think with collies you need to be confident in your own ability otherwise they pick up on it. Do you feel a bit nervous? have you had a collie before? I am no expert, just a collie owner, but all my collies have liked
a) routine (feeding times/walking/bed - they love routine, they think about it before you do)
b) consistency (ie. write a list of words you will use to train and everyone had to use the same word/sign) You need to be consistent all the time with them, no letting them get away with stuff because it only takes once and they are in for the long haul of training you :o Everyone in the family needs to be using the same language/instruction
c) exercise and brain games. Get him used to fetching a ball if can't - collies love ball games - this will also wear him out
Look at what you are feeding him. Nothing coloured at all with a collie otherwise it ends in all sorts of behaviours you don't want. I think raw diet, butchers tripe, chappie is about it....we feed ours chappie - it has always been fine, just watch treats (we use cooked chicken)
As for the mouthing, collies can be prone to this tbh, but we make a high pitched yelp and turn away from the dog and do not interact. They soon get used to not doing it. There is a good book called 7 steps to puppy school (or training) which is good for just generally positive training techniques, but the class will help too, really don't worry!
As for the crate, carry on using it, they area great tool and he might just feel safe in there as he doesn't know who you are yet :) it must be ever so confusing for them after an unsettled start
Lastly, enjoy it. You put the work in so will he, they are incredibly loyal and wonderful dogs in the right hands and they are trainable, don't woprry if you are not an experience collie owner too as everyone has to start somewhere. I grew up with collies, but having my first rescue collie was a learning experience until she died (aged 18!) tbh. But they are fantastic dogs and you really do get back what you give with them
Wiccaweys has lots of great advice on their advice pages about collies too. It will all be fine you know, it just takes time