Okay, so today I bought the game on PC and I have only finished 2% but I have a few questions 
1.What are riddles? The game says I have completed 4 but the only thing I have done is found ? marks no question or anything.
2. How do I get new moves? do I need to buy them? if so how come the game wont tell me how much it is and there is no 'Buy' button?
 
Thanks.

The riddles are essentially the Riddler trophies and also questions that will pop up from time to time. You can check them in the menu. 
 
The only new moves are things like the Inverted takedown which you get through upgrades, so that's only once you have enough XP to level up.

1. The best way to find these joker riddles or these trophies, question marks and stuff is to find the riddlier's map for each area. You go into the options or whatever, you will see a map with all the riddles you haven't solved yet. Also you have to scan certain areas for clues, lining up a question mark you can only see with the bat vision mode, or just scanning stuff that's mentioned in the riddlier's map. Remember when that cop was killed by the joker near the beginning and you have to scan that portrait on the wall? Do exactly the same thing with objects the riddlier mentions for his clues. If you are near a puzzle, the riddlier will at least let you know by saying something, like it's the enigma show then it will give you a quick clue. Honestly getting the map which is near the end of every building you fight at will point you in the right direction. Without that map, it's honestly difficult finding everything. 
 
2. You have to get enough points from fighting and doing combos well, then you can upgrade. It's on your lifebar, I think it's the white bar that goes in a circle. You then can choose an upgrade you want like better armor, double batarang and stuff like that. The fastest way to get more points is to solve the riddles or find those question marks on the ground which is getting the riddlier's map.

1. When you reach the point when Riddler hacks into your primitive communications another tab will be added to the map screen that will list all of the riddles for the area you're currently in.  You can change which area to view by clicking the left and right arrows in the corners of the area screenshot.  The riddles with animated icons are located in the same room you're currently in.
 
2. After you acquire enough XP, as indicated around your health meter, it will prompt you to upgrade.  Press Tab and you'll be presented with the upgrade screen.

Riddles are either question marks you find or other times certain areas you have to scan. No actual puzzle solving, aside from figuring out from what position to scan certain later "riddles". Quite underwhelming, yes. And what the guy said above about tab.

I have a question as well:
 
Why is Batman so awesome?

" I have a question as well:  Why is Batman so awesome? "