When choosing a commander, you must use either a legendary creature, a planeswalker with the ability to be commander, or a pair of legendary creatures or planeswalkers that both have partner. The chosen card or pair is called the commander or general of the deck.
Generally you can only have one commander, but a player can have two if both have the partner ability. Because both commanders start the game in the command zone, the remaining library is only 98 cards. Until today, you can't have 3 or more commanders.
Yes, any creature that enters the battlefield from anywhere suffers from Summoning Sickness unless otherwise stated.
A planeswalker can be a commander if the card says that they it can. Most planeswalkers cannot be a commander because the rules committee banned them from being commanders. However, Wizards made some planeswalker cards that can be commanders stated in the card ability, but they are the exception.
If your commander would be exiled or put into your hand, graveyard, or library from anywhere, you may choose to put it into the command zone instead. Since you can choose, it can go to exile if the player wants.
Even if you choose to make your commander go back to the command zone, with the new rules, the commander actually goes to the graveyard or exile zone before going to the command zone. Triggered abilities that care about creatures dying or going to the exile zone now happen.
If a commander deals 21 combat damage to a player, that player loses the game. Commander abilities will not count towards the damage limit as it only counts combat damage. This means that if you use Niv-Mizzet, Parun, whenever their ability is triggered and deals damage, this is not counted towards the 21 damage limit.
A Commander deck consists of 100 cards and you can’t have more than one of any card that isn’t a basic land. You cannot have neither more or less than 100 cards in total.
The sideboarding rule for Commander is optional; if it's used, your sideboard can be 10 cards. The sideboard must obey all the other deck construction rules, so you can't put duplicate/additional copies of cards in it or cards you otherwise wouldn't be allowed to put in your main deck in the first place.