Can I install a (probably ductless) range hood against brick?
There's no reason you can't install a hood on the brick, it will work fine. You need to buy one designed to hang on the wall, not the ceiling, and there's loads of choices either way. You can run a power line up from behind the range and hide it with a splashback. I highly recommend a splashback instead of having bare brick as it will be much easier to clean food off of. 

As for ducting it completely depends on the construction of your home how possible it is to do, and how cosmetically pleasing you can make it. It's not possible to say without more detail. 

Before making any decisions you should check your local building codes, some areas mandate you have to install a duct, others don't. Some mandate you can't have your range in certain places. It would stink to build your kitchen and then find out it's illegal!