yes you can use his effect in battle phase
No you cant
It says on the card that it is used during the opponent's battle phase. Yes, it can be used in the same battle phase it is summoned in, there is no restriction against this.
AnswerYes. He attacks on the saame turn he is special summoned because it is still the battle phase.This is also the case for Cyber Jar. When the Cyber Jar effect resolves the monsters that you special summon in attack position can still attack because you are still in the battle phase.
Yes of course. As long as they were special summoned before, or during the battle phase.
As long as you are Special Summoning before, or during the Battle Phase, then yes, that monster can attack.
Polymerization is a spell speed 1 card. You cannot activate it in your battle phase at all.
Not exactly. You can proceed from Main Phase 1 to the End Phase if you don't wish to have a battle phase, that is valid. You will skip the Battle Phase and Main Phase 2. But if you DO have a Battle Phase, then you must also have a Main Phase 2. A turn player can ask the opponent if it's ok to move to the end phase from the battle phase if he doesn't want to use Main Phase 2. That allows the opponent opportunity to say no, if they wished to activate something there. But the phase is not being skipped, in the same sense as the example above.
Unless another card specifically denies the attack or if it was Special Summoned AFTER the Battle Phase, then yes the Special Summoned monster may attack.
Yes, it can be activated during your opponents battle phase.
Horus Lv6 says, that at the End Phase of the turn in which it destroys a monster by battle, that you can send it to the graveyard to special summon Lv8. This means Horus Lv6 must still be on the field after the battle phase, all the way to the end phase. If it gets destroyed during the battle phase, then it cannot summon Lv8.
Unless specifically stated otherwise (like on Gorz, or Battle Fader) a special summon can only be performed at the same timing as a Normal Summon, ie, in your own main phases when there is no chain in progress.
YES!! Because you have both a main phase 1 and a main phase 2. If you do not summon a monster in main phase 1, enter your battle phase, complete your battle phase, then enter your main phase 2 and you can summon a monster with 4 stars or less unless it has a special effect or tribute the monster that already attacked. Unfortunately you will not be able to attack with the new monster until the next turn, but hey, thems the breaks.