I mean I target an opponent, he copies the spell and targets me, then I copy the spell and target him back, etc... More, can I target myself and copy the spell to myself and again?
Yes, Chain of Smog works that way - whoever you choose to target can copy the spell, and whoever they choose to target can copy the spell, and on and on and on. Note that this does not constitute an "Infinite Loop" as per the rules, however, as these are not mandatory actions that will repeat without intervention. Each player targeted by Chain of Smog has to choose whether or not to copy the spell or not, so the loop doesn't just run forever without intervention. Even if you target yourself, you could choose to copy the spell 1 million times, but you can't choose to copy an infinite number of times to force a draw.
Yes, Chain of Smog can be chained indefinitely between opponents, or one player can chain it on themselves indefinitely.
Any copy of Chain of Smog does the same thing as the original. That includes that the targeted player may copy the spell and choose a new target player. Since the spell requires a target player, as opposed to a target opponent, either player may also target themselves until they choose not to copy or target a different player.
Note that as long as nothing in the game cares about the number of spells that resolved, once both players are out of hand cards, further copies of Chain of Smog don't change the game state, and therefore the back-and-forth must end due to the shortcut rules:
720.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.
That means that once both players are out of hand cards, and both players have copied the Chain while their respective opponents had no cards in hand, the active player must stop copying the Chain and do anything else.