Since patch 1.9 there is no maximum level anymore.
If you have a skill at 100 you can make it "Legendary". This resets the skill to 15, gives all perk points invested in that specific tree back. Be warned: You lose all the benefits of having a higher skill level! The advantages of making skills legendary are:
- Difficulty increase, since the enemies don't have their skills reduced.
- You can continue to level up and earn extra skill perks.
It is possible to repeatedly make a skill legendary or to make multiple skills legendary, this allows you to (slowly) unlock all perk points.
Level 81 is the maximum level in Skyrim without making any skill Legendary
There is a linearly constant amount of "experience" required for each level. The formula is simply:
(level-1) * 25 + 100
Where level is your current level.
"Experience" in this case is earned strictly through skill ups. Leveling a skill to X will give you X experience towards your next level. For instance, to level from level 1 to level 2, you require 100 experience. This means you can either raise 5 skills to level 20, one skill to level 21 (assuming it starts at 15), or any other permutation thereof.
Also, and this is important:
There is no soft cap
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Level 81 is just as (relatively) easy to reach as Level 11, it just requires more total experience.
Since all races have +10 to one skill and +5 to five skills, this means there is a total of 88,085 "experience" to earn, and this is constant across the ten races. Level 82 would require 89,100 total experience, and is currently unreachable.
Thus, when your character maxes all of their skills, they will be level 81.
I could find no credible sources about this, so I performed a completely unscientific experiment to figure this out:
I loaded up a low-level saved game and used Flame continuously until my magicka was exhausted, then took a screenshot of the skill screen. I then reloaded the game and used Flame in ~1 second bursts until my magicka ran out, and took another screenshot. I then compared the pixels in the screenshots using Paint, and determined that they had both advanced an equal number of pixels. This suggests that it's extremely likely that it doesn't matter if you cast with duration or frequency - you'll gain at the same rate.
In summary, there is most likely no difference.
Best Answer
As Ben said, you can still gain experience and level up individual skills. However, yes, your level only goes up after you have selected to level up. The wiki offers much more information.
To answer your other question:
For all intents and purposes, yes. There is a really good answer already for this here, so I will not rehash.