Which one sound sounds more natural in speaking?

The second one sounds much more natural and is how I’d say it

The second one is what I’d say

The first one sounds more formal to me (although I’m from the U.S), the second one sounds more natural.

I prefer the 2nd.

The second one, although I feel like in English it's more natural to answer the query and then provide the reason, e.g. "I can't do that right now because my laptop is being repaired."

You can say the specific name of the business, or (US) you can also say "the shop." Usually the shop means an auto garage, your car is being worked on, but you can use it to mean that some other machine is at a place where it's being repaired. My car/computer/lawnmower/vacuum cleaner is in the shop. is idiomatic.

Second one. I might say ‘My laptop’s in for repair’, but I wouldn’t say I’ve ’left it for repair’.

I'd say "my laptop is in for repairs" but the second one sounds more natural out of the two options

The second is better, though if you want to be extra casual about it you could say: "My laptop's in the shop, so I can't do anything at the moment."

The latter. At least in the US most people will "drop off" their computer for repair, not leave it.

Normally I'd go for the second one.  I might use a less formal version of the first if I wanted to emphasize timing or sound more apologetic: "Oh, damn, I just dropped off my laptop for repair, so I can't..." meaning, I could've helped if you'd asked a little earlier, but unfortunately you've missed your chance. 

Definitely the second one.

It would sound more natural to say "My laptop is broken". They should be able to figure out that you can't do anything on your laptop.

"Laptop's in the shop. Can't do anything until it's fixed."

Depends, is it possible that the laptop isn't being repaired at that moment, but both of them are correct anyway

If you wanted to be very casual you could say: My laptop’s in the shop, so I can’t do anything right now

The second sounds more natural. With the first I expect you to include location information because you used the word “left.”

Definitely the second one. "Left for repair" sounds both stiffly formal and like an incomplete thought, somehow.

I would probably say fixed rather than repaired as an American native speaker. My laptop is getting fixed.