Yes. To 'return' a card to the main deck means to shuffle a card back into it.
The Deck is shuffled whenever something is 'returned to' it, or removed due to a search effect. Yes, it must be shuffled after another Gladiator Beast is Special Summoned on resolution.
shuffled can be used as a deck of cards "the dealer shuffled the deck of cards before dealing the game of poker"
The New York train then shuffled off to Buffalo. The card dealer just shuffled a new deck.
I would only do it when the deck is re-shuffled.
With a well shuffled normal deck, it is 16/52 or 4/13.
Yes. Kasha's effect to return all monsters to deck is a triggered effect, triggered on special summon. Fiendish Chain can be chained to this, and will resolve first. That means Kasha's trigger will be negated when it tries to resolve, and nothing will be shuffled back into deck. Kasha's ATK will remain at 0.
Since hearts and clubs consist of 1/2 of the deck of cards, the probabilility of getting hearts or clubs on a single pick from a well shuffled standard deck of cards is 1/2.
It could be used in a variety of ways such as "I shuffled down the hallway to class," or it can be used as, "I shuffled the deck so that the cards would not be in order."
4 out of 52, or 2 out of 26, or 1 out of 13..
1/4
There is a 1 in 52 chance that the first card drawn in a standard, shuffled 52 card deck, will have a value of 7.
A best yugioh deck would be a deck that eliminates your opponents options. like a deck with jinzo and horus, the black flame dragon LV 8 both can stop your opponents spell and trap cards. also a deck with cards like needle worm can discard your opponents deck so when they have no cards left you win.