#1: He's not too young to start training. Keep your expectations reasonable though - he's only going to know what you've taught him, and his attention span is going to be very short.
#2: He's not "stubborn". He's still a baby and he doesn't yet know what you expect of him. Training is a process that takes some time. Stubborn can only be a factor when he's 100% sure what you're asking of him and he refuses to comply. I can guarantee that at his age, that's not what's happening.
Whether or not you use a crate is entirely up to you. There are many good reasons to use one, however. Whenever I couldn't be actively supervising my puppy (taking a shower, cleaning house, at work, making dinner, eating a meal?) puppy went in the crate. Housebreaking is much easier with a crate, as is preventing destructive chewing, which can be very expensive and potentially life threatening.
If you need to leave your dog at the vet for any reason, it's going to be easier on him if he's crate trained. Also, if you ever plan to travel and need to leave him in a hotel room, or if you're going to participate in any dog sports, he'll need to be in a crate. My dogs were crated when not being worked at nosework classes, and Halo is in a crate at flyball practice every week. We've traveled out of town for flyball tournaments, which involved staying in hotels and crates. Do you ever want to take him to someone else's house, either for a visit or an overnight stay? Your hosts will appreciate him being in a crate when you can't watch him.