The target opponent may still cast spells in response to Xanathar, Guild Kingpin's ability in your upkeep. If that player has somehow become an illegal target for the ability as it tries to resolve, the ability does nothing. They may cast spells and you cannot look at or play the top card of their library.

You'll still pay all costs for spells cast this way, including additional costs. You may also pay alternative costs if any are available.

During your turn, you can look at the top card of the chosen opponent's library whenever you want (with one restriction; see below), even if you don't have priority. This action doesn't use the stack. Knowing what that card is becomes part of the information you have access to, just like you can look at the cards in your hand.

If the top card of that library changes while you're casting a spell, playing a land, or activating an ability, you can't look at the new top card until you finish doing so. This means that if you cast a spell from the top of that library, you can't look at the next card until you're done paying for that spell.

Xanathar doesn't change when you can cast spells or play lands. You must still follow all normal timing rules and land play limits.