If you buy skill training in one of your major skills, do you come closer to leveling up?
Also, if say, you buy restoration skill, do you get a greater + to willpower when you sleep and level up, or strength if you train blade?

I do believe that training does count towards your level up.

I'm not sure if it counts towards your attribute bonuses, but I'd imagine it would.

It depends on what your level is, in the skill that you are training....
Willpower is separate from restoration. Restoration is a skill. Willpower is an Attribute that governs the restoration skill among others. If you train your restoration skill, and destruction and alteration spells, to the point where you receive a combined ten skill increases in those skills (it can be any combination: 4 skill ups in restoration, 3 in Destruction, 3 in Alteration for example) you will be able to increase your Willpower attribute when you level up, which governs in part fatigue, and how fast your magicka regenerates..... Make sense?

Training does count towards your level up and your attribute bonus.

Indeed

Thanks.

One nice thing about the way purchased training works is that you don't even have to be capable of doing what you're training. You can get Marksman training without ever having a bow or arrows in your inventory, let alone shooting one.

If you've got more gold than you can spend, and there's an attribute you want to increase at your next level-up, but you have no hope of using that skill enough, then buying training makes a lot of good sense. Since Agility helps a swordsman keep his balance, buying Marksman is useful once Strength and Endurance have been accounted for by using his everyday skills. He'll have to sneak and lockpick for the other half, or settle for +2/3, but it helps.

If you buy too much, of course, you'll end up highly skilled in something you don't do, but that's not really a problem.

Oh, and I usually buy Mercantile Training if I have spare training sessions available, because it pays me back pretty quickly, so why not?