I want to know how i can check if a player has a certain item in his inventory, and also how to remove items from a players inventory

If you are referring to your own items (mod-made) you can override Item.onUpdate() method which is launched when you have it in inv.

 

If you need to know if any item is in inventory use PlayerTickEvent and scan through inventory for item. If you would have hard time figuring it out please write.

I managed to find what i needed, but now all i need to know is how to add an item into a players inventory.

entityPlayer.inventory.addItemStackToInventory(new ItemStack(MyMod.myModItem, 1));

Thank you very much!