Nalia doesn't change when you can cast spells. Normally, this means during your main phase when the stack is empty, although flash may change this.

You'll still pay all costs for the spell, including additional costs. You may also pay alternative costs if any are available.

You can look at the top card of your 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.

After the last ability has resolved, no longer having a full party won't cause any of the creatures that gained deathtouch to lose it.

Nalia's last ability will check whether you have a full party at the beginning of combat on your turn. If you don't, the ability won't trigger. If the ability does trigger, it will check again as it tries to resolve. If you don't have a full party at that time, the ability won't resolve and none of its effects will happen.

You have a "full party" if the number of creatures in your party is four (that is, you control a Cleric, a Rogue, a Warrior, and a Wizard, and they are four different creatures).

If the top card of your 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 your library, you can't look at the next one until you're done paying for that spell.

The top card of your library isn't in your hand, so you can't take other actions that would normally be allowed from your hand, such as discarding it due to an effect or activating a cycling ability.