1. Yes. Expect (many?) dozens of items per skill point increase. Carpentry is very frustrating because it can only be increased through pointless grinding, as you very quickly reach the point where you've produced all the items you actually have any use for. Because of that I've modified the Buiodda's Crafts mod to use a lot of carpentry and wood crafting as skills for tasks (using carpentry as a detailed handiwork skill and wood crafting as a heavy one).
2. There is a skill increase indication showing you've successfully increased the skill, but it's still capped at 100, so it doesn't achieve anything. The only place where I think this matters is in one of the game courses, where it allows you to succeed in the task to increase the archery even if it was 100 beforehand (which is extremely unlikely).