mirror force
crush card virus
trap hole
sakeretsu armour
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seto, kaiba and pegasus give out really good trap cards like crush card and such.
Normal Monsters Effect Monsters Fusion Monsters Ritual Monsters Synchro Monsters XYZ Monsters Spell Cards Trap Cards
"Botttomless Trap Hole" is typically viewed as being better than "Trap Hole" since the destroyed monster in banished/removed from play. A majority of cards function off of cards in the Graveyard or even activate in the Graveyard, so banishing the monster would be more disruptive. That being said, "Trap Hole" can destroy monsters with an ATK under 1500 unlike its "Bottomless" counterpart. Plus there are a few monsters like "D.D. Survivor" that function better when removed from play.
If you mean Union monsters then yes they do, as will any monsters turned into Equip cards by monsters such as Destiny Hero Plasma or Koa'Ki Meiru War Arms.
You have five monster slots on your Field, so even a card that can summon an unspecified amount of monsters (like Return from the Different Dimension) you will still only be able to summon a maximum of 5 to your own side of the field. There are no cards that can increase this, and Trap Monsters take up a monster card slot so it's not like you could have five regular monsters and an Embodiment of Apophis.