You can only do so if a card effect specifically lets you, like Call of the Haunted.
Otherwise, regular Special Summons, Synchro, Fusions, XYZ's, etc, all must be done on your turn in your own main phases.
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Yes, a Special Summon of any kind does not count towards your limit of one Normal Summon or Set per turn. You can Special Summon as many times a s you want per turn.
You are allowed one Normal Summon per turn, and as many Special Summons as you have the resources to perform them.
Yes, you can, as a Synchro Summon is a special summon, you can perform a Normal Summon on the same turn as one or more Synchro Summons.
Not quite. A Synchro Summon is a Special Summon. A Tribute Summon is the same as a Normal Summon, except that when you Tribute Summon you need to tribute monsters. Also you can Special Summon as many times as you want to in a turn, whereas you can only Normal Summon OR Tribute Summon once per turn, except with a card effect.
Yes, of course. You are allowed to perform as many special summons in a turn as you've got the resources to do so, Synchro and Fusion summons are kinds of special summon.