Could/should you use a foundation brush for tinted moisturizer?

Yes, you can. It'll do exactly the same as it does with foundation, allowing more and less coverage where you need it.

I tried it and it does not go on too well. Its better to use your fingers, start from the centre of your face and blend outwards. The warmth from your hands makes it look more natural x

Yes

I love tinted moisturizer. I just bought some for the first time and made the switch from liquid foundation to this and i will never go back. It is light and it covers my flaws but does not make my face look like a cake. When i bought it, i bought a foundation brush, but after using the brush, the moisturizer and even foundation sat into my creases making me look old and it made me look like i was wearing a little too much foundation. It looks a lot more natural when i just use my finger.