QIf my opponent's deck is empty, and I make them put the top card of their deck into their cemetery, do I win the game?

ANo. If you draw a card when your deck is empty, you lose the game. If you put the top card of your deck into your cemetery when your deck is empty, nothing happens.

QCan you explain this follower's activated ability in detail?

AIf you can select a card in an opponent's cemetery, you can pay 8 play points to play this follower's activated ability, by which you play the selected card for 0 play points.

If you selected a follower or amulet, you put it onto your field and play any Fanfare abilities it has. When it moves to a zone other than the field, it moves to the corresponding zone of its owner. Cards put onto your field with this follower's ability are generally treated in the same way as stolen cards. See the Q&A for Angel of Chaos (BP03-109EN) for more details.

If you selected a spell, you resolve its abilities, then put it back into its owner's cemetery.

QIf I play Dimension Shift with this follower's activated ability, do I put it back into my opponent's cemetery after resolving it?

AYes, you do.

QCan I select and play 7 More Centimeters with this follower's activated ability?

AIt depends. First, you can select 7 More Centimeters from an opponent's cemetery. Then, if you have at least 20 Umamusume cards in your cemetery, you can play it for 0 play points. If not, you can't play it, and nothing else happens.