First of all baby proof as much as possible...put everything up high until you run out of high
Use gates to keep him in the main areas and keep those areas safe. I have a kitchen, dining room, livingroom area that is pretty much a free for all.
Then keep tons of stuff around for him to get into...board books, toys...just stuff...
Take him around and show him things if he wants to see them.
teach him gentle touch
put the Chinchilla away in a safe place until he learns gentle touch
Don't do anything you are not in the mood for. For example if you are having a tiring/sick day don't expect too much. Don't do laundry or clean or try to do stuff that you really don't have patience for.
Biting..Sophia bit...especially my boobs...what worked? Watch him carefully for a while to see what triggers it and be mindful of when it is about to happen. For Sophia I had to give a very "boring" response..."do not bite, it hurts" and then remove her from me for a while.
Try not to use the word no too much, instead show him what he can do
Ask yourself "why" he can't have certain things...most things he really can. And if you are worried that he will expect to have them always because you let him do it, well don't. He will become bored with whatever it is and move on to something new.
Don't worry about who is watching...you don't always have to do something because others expect it.
Tell him you understand how he feels when something that is non negotiable frustrates him. Learn what he needs to get through his meltdown instead of trying to stop it.
TEach him how to transition...I taugh t my kids to say good bye to things Like playgroups, sandboxes, things they can't have etc.
Teach him how you want him to do things..instead of telling him not to do do something.
Show him how to pet the Chinchilla properly under your supervision.
Don't worry about how he will "turn out", enjoy him now..you can't spoil him by loving him and teaching him and redirecting him instead of punishing him.
and of course always ask for help when you need it.
I second Alphie Kohn Unconditional Parenting as a book but am not a big fan of Sears for the older child...but for AP he is great.
Oh...as an added note..the way he is behaving now is not a discipline issue..it's a ten month old baby issue but reading up now will help you later on for sure.