You can drain skills to get cheaper training at any character or skill level. Not clear if that is a "glitch" or works as intended.
Although your numbers go higher than 100 in your menu, it doesn't actually do anything, save the acrobatics and athletics skills. Same deal with attributes. ...
It is true that except for acrobatics and athletics, skill about 100 have the same effect as skills at 100. So no real point.
But it's different for attributes. They do show benefits above 100:
Strength: you can carry more and have more "fatigue", aka stamina. But no more Blade, Blunt or H2H damage
Intelligence: more magicka
Willpower: faster magicka regeneration (except for atronachs of course) and more fatigue/stamina
Speed: faster movement
Agility: more fatigue/stamina, but no more bow damage some say you might be able to sneak better and have less staggers, but that's unproven I think
Endurance: more health points. more fatigue/stamina
Personality: higher starting disposition I think, but it doesn't really matter
Luck: some misc effects like Mehrunes Razor and Arena betting