Yes.

You can only trade a game in your inventory. A game that is activated (in you Libray) can not be removed from there and can not be traded.

During checkout, you have to option to buy for your self or as a gift. If you chose the Gift option, there is another option to chose who it goes to. One of them is for adding it to you inventory.

If a game has been added to your library, then its yours forever and it cannot be traded.

You can have games in your inventory that can be freely exchanged.
Some in-game items can be exchanged too (sometimes for games).

You can directly purchase a steam game from the steam store, or have it stored in your inventory, or sent to someone else (You decide at the time of purchase).

Some people have lots of alphanumeric codes that are equivalent to the games that sit in your inventory. However no way to tell if a code has been entered onto steam (by anyone else) or if its invalid, or even what game it is before you type it in. If the code works its final. A list must be maintained of what code means what game. Some people lie and offer you a game you want(Portal 2) but when you enter the code, you get something else (SnuggleTruck).

Some in-game items can be placed on the Steam "Market" where if it sells, you get virtual money to spend on games (Steam Wallet).