Is the hot water line always on the right

Nope, usually on the left. If your pipes are reversed you can usually turn the cartridge 180 and reinstall to correct the error.

Is the hot water line always on the right

Every hot line in my house, US, in every bath, sink, or appliance, has hot on left.

"Is the hot water line always on the right" Hopefully you read my previous answer. The hot is on the left as you face the mixing valve. If you have two faucets, one hot and one cold you could reverse them if you have some special reason but plumbers install them hot on the left.

Here's a bit of plumbing trivia for you. There's a reason that cold water's located on the right. Many years ago before water heaters hot water was heated on the stove in the kitchen. Cold water was pumped to a storage tank and piped to the kitchen sink, (toilets were still outhouses back then so the kitchen sink was the only water source.) Since most people are right handed it was only natural to put the cold where it was easily reached. Cold water has remained on the right ever since. And now you know the rest of the story. Cheers, Tom