Yes. TF2 is a GREAT game, and I recommend you "buy" it.
TF2 is now free to Play.
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No you cannot trade weapons for beta tf2 to normal tf2. Beta Tf2 is considered to be a completely different game by steam. Therefore the two game's inventories are not compatible.
Try lowering your graphics settings.
Weapons cannot be "leveled up" in TF2
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It is unknown as of yet.