not recommended especially with a renovation where you have a chance to pick the same finishes.

I think matching is a personal preference. Generally, I think of lighting as jewelry and you have a bit more freedom. I do like plumbing fixtures to all match. You will see a lot of kitchens with chrome lights and brushed nickel or stainless elsewhere, and I am assuming if you search houzz bathrooms you will find that combination as well.
https://www.houzz.com/magazine/how-to-mix-metal-finishes-in-the-bathroom-stsetivw-vs~3828529

Sure!

Generally the trend is to have all of the finishes the same, especially in a remodel, but I have seen (and as a professional would consider) mixing finishes. There needs to be balance... if everything is brushed nickel except for one thing, it may look like you just forgot that one item.