yes becaus a syncro summon is a special summon as is a fusion summon
Yes, unless the card itself or another card on the field says so, a monster can attack on the same turn it was Normal or Special Summoned.
He can be Tributed by his own effect to make Effect Damage 0, but he cannot be Tribute Summoned on the same turn he's Normal Summoned because you can only Normal Summon once per turn. (Sorry if I sound too obvious) His effect doesn't activate if you tribute him for other effects.
Yes, a monster can attack the turn it is Normal, Flip, or Special Summoned unless it says otherwise.
Yes, there is nothing inherently within the tributing or summoning rules which would stop you from tributing a monster you summoned the same turn you summoned it. Obviously, due to the regular summon rules, you can not Tribute Summon the monster you just Normal Summoned on the same turn; it would count as two Normal Summons. But if the first summon was a Special Summon, you had used "Double Summon", or wanted to tribute it for an effect like "Enemy Controller", then it's totally fine to tribute that monster for them.
Yes you can normal summon turbo booster, but only when you haven't normal summoned in the same turn already. Rather than being a 'special summon-only' monster, Turbo Booster's special summon is a case of 'you can' do it, if you wish. Like Cyber Dragon, it is a monster who can be Normal Summoned, but has an alternate, special summon method too.
Winged Dragon of Ra must be normal summoned. It doesn't actually matter about turns, just as long as you keep the 'one normal summon/set' per turn rule in mind. You could special summon all three and then tribute them to Tribute Summon Ra. But if you normal summoned the third monster, then you could not Tribute Summon Ra that turn unless you had a way of granting more Normal Summons, in which case yes, you could do it.
No, a monster cannot manually change battle position on the turn it was special summoned, though it can be changed by an effect.
no it can not
Tsukuyomi is a spirit monster, right? All spirit monsters return to the owner's hand at the End Phase of the turn that it was Normal Summoned or Flip Summoned.
Yes, this is legal. You may perform one Normal Summon or set per turn, and as many Flip Summons as you wish.However you cannot Flip Summon a monster Set that turn, nor if you Flip Summon a monster, turn it face-down in the same turn using an effect, can you Flip Summon it again that turn. Lastly if a monster declares an attack, and is flipped face-down in response, it cannot be Flip Summoned that turn.
The answer to this question can vary. Unless the card that Special Summoned the Gemini Monster specifically says otherwise, the Gemini Monster will be treated as a Normal Monster. If you have not already Normal Summoned this turn, you can perform said action on the Special Summoned Gemini Monster. There may be cards such as Black Brutdrago that states "The Special Summoned monster is treated as an Effect Monster, and gains its effect." In this case, as it states, the Special Summoned monster gains its effect while it is on the field and you do not have to resummon it.
Obelisk can. Ra can't be special summoned though.