Yes, this is absolutely fine. But you may want to consider using low voltage lighting. That has the advantage that many (most) of the rules are relaxed. Your high voltage (120V AC) to low voltage (e.g., 12V or 24V DC) power pack has to be wired properly, but beyond that you have a lot more freedom, because the risk of damage to wires (fire or electrocution) is far lower.

In general though, unless you are in a place like Chicago, you may not even need much conduit. Conduit serves two purposes - it protects individual wires (which always need protection) and it protects NM cable (a.ka. Romex) (which needs protection in certain locations.) NM cable can be protected in other ways, and where it is high up or in the wall, etc. it doesn't need any extra protection at all. But conduit is always a safe and legal method.

Yes, this is absolutely fine. But you may want to consider using low voltage lighting. That has the advantage that many (most) of the rules are relaxed. Your mains voltage (120V AC) to low voltage (e.g., 12V or 24V DC) power pack has to be wired properly, but beyond that you have a lot more freedom, because the risk of damage to wires (fire or electrocution) is far lower.

In general though, unless you are in a place like Chicago, you may not even need much conduit. Conduit serves two purposes - it protects individual wires (which always need protection) and it protects NM cable (a.ka. Romex) (which needs protection in certain locations.) NM cable can be protected in other ways, and where it is high up or in the wall, etc. it doesn't need any extra protection at all. But conduit is always a safe and legal method.