No not the creature, the spell it allows you to cast
It can't be combined with other alternative costs, such as casting a spell "without paying its mana cost." You may, however, pay additional costs, such as kicker
Regarding your mana base, Lotus FieldLotus Field, Adagia, Windswept BastionAdagia, Windswept Bastion, and Nykthos, Shrine to NyxNykthos, Shrine to Nyx aren't mandatory
Card advantage is a strategic concept (rather than a specific game term) and a lot broader, and basically means having more cardboard than my opponents. For starters, any card that puts more cards in your hand is card advantage, even if it doesn't say draw. But card advantage also looks at what happens in other zones
4 Omniscience You See Everything For ten mana you would expect a spell to be exceptionally powerful, and thats exactly what you get with Omniscience
If a creature card was exiled this way, you may have Lazav become a copy of that card until end of turn