Re: The difference between Tenkai and Kaiten
My understanding is that tenkai and kaiten mean exactly the same thing (although I don't hear kaiten very often?)... it's when you rotate your body 180 degrees by twisting your hips without taking steps (unlike tenkan). Personally I often hear both tenkan and tenkai used to refer to what's technically irimi tenkan or irimi tenkai (i.e., step forward and then tenkan or tenkai)... sometimes people don't specifically say irimi, I guess because it's obvious from the context.
As far as I have always heard them used, tenkan, tenkai, and tenshin (and irimi, and soto tenkan, etc) are basically just the names for steps you take or different ways you can displace your body and all are used as building blocks in many many many different techniques.
Uchi and soto I believe mean 'inside' and 'outside' so they refer to two different versions of a technique where one you enter 'inside' (e.g., by extending their arm and passing through the opening you've made) and the other 'outside'.