1. The battery should be in the trunk, so you just need to tap into those. Or add you own connectors to the battery (don't forget to fuse them)
2. I have moved my HU to the glovebox (E36 328 '97), but it is not a factory one. It is normally possible to run without a HU but you will need to check which audio system you have on your E46, there has been discussion on this board about that.
3. Down the middle under the carpet or down the sides under the trim. Make sure you run Audio down one and power down another.
4. Define cold weather. Again there has been discussion of this on the board, so have a search and see what reports there are for the kind of temperatures you expect.
Really low temperatures can cause HD's and screens to be sluggish or not work till they warm up. High temperartures obviuosly cause the CPU and/or PSU to overheat and cut out.