Yeah the outdoor unit can go as high as you want. I got a mounting bracket for mine, it came with expansion bolts, which provide a VERY strong fixing into brick. However, as has already been said, I wouldn't go for a DIY split again. They are prone to leaks, and aren't very powerful. I certainly wouldn't trust the quoted output after the first year.
The best you will get is a split unit from a local air con installer. But look at around £1000 for this. A very rough figure, maybe more, maybe less. Bear in mind, this would have an integral heater, which would use the refrigerant circuit in reverse - this is a very efficient way of heating a room. Up to 400% on a good system.
For occasional use, a branded stand alone unit with exhaust hose would be a good idea. But these dont always have a heat function - they are noisy anyway.
Does the outdoor unit have to go on the wall directly outside? Could the pipework be routed elsewhere, round the corner? (with a pro fit system, the pipework length can be a lot longer)