1. you can go as low as the minumum system requirements of your software / os.
2. older tech is going to be bigger, i wouldn't expect to velcro it to anything.
3. nothing would be cheaper than a Pi, there are some compeditors and their names escape me right now. look for "pico itx" and "nano itx". some of these are $300-$500 range, but are turn key devices. all hardware and software installed.
4 see point 2. keep in mind, older tech is also much more power hungry/wasting than anything new.