Monster Reborn is a Normal Spell Card, so is Spell Speed 1. You can only activate it during your own Main Phases, as the start of a chain.
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As long as you summoned it with Monster Reborn in main phase 1, then yes, of course. If you summoned it in main phase 2, you cannot attack because you have already passed the battle phase.
Monsters can only 'manually' change battle position in your main phases. If you want to change them during the battle phase, you will have to do it by a card effect.
As long as you are Special Summoning before, or during the Battle Phase, then yes, that monster can attack.
Magical hats can only be used during your opponent's battle phase. Seeing as they can't flip their monsters during their battle phase, no. However, if your opponent does activate a spell or trap card during the battle phase, you can use Magical hats and protect your monsters. Overall, yes. You can use magical hats to protect your monsters from targeting effects as long as it's during your opponent's battle phase.
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.