when rise a level will my limb condition and health get healed?

No. Though the health-point meter adjusting to your new hit points that you gained from the level up may look like you got more health out of nowhere.

when you play FNV for the first time, a bit misleading when you see the loading title on the screen about "eating food slowly restores health...", indeed it does, but what you dont know is that it wont restore limb condition like sleeping/stims do.
the first time i played FNV, i was led to believe that eating food would slowly restore damaged, not crippled limb condition as well, obviously not the case after a long while of trying, although this would have been a good idea in the game.