I like khajiits so I make one particular stealth build with same looking khajiit but I like heavy armour shield wielding warrior but anyone have done khajiit warrior? Does it take long to compensate those skills?

No, it is more flavor. The only lasting difference outside appearance is their racial power and abilities. Same as earlier games really.

No, it does't take long at all to compensate for anything. Every single race in the game has the same attributes and the bonuses are so worthless that it will only take you 4-5 dungeons to make up for them.

You can use whatever race you want and just go from there using whatever skills you like. Just disregard all the characater bonuses because they can be overcome very quickly.

You'll actually level up faster because your base stats are faster to increase, but you'll be weaker than let's say a nord or orc, but not for long

Not really true, as higher level skills give you more XP than lower level skills(i.e. increasing a skill from 20 to 21 will give you 1/4 of the bar to get to level 2; increasing a skill from 25 to 26 will give you 1/3)

The Racial Differences are such that if you develop your character to enhance those differences, then they matter. If you develop your character to overcome those differences, then they don't matter other than appearance.