Everyone has old routers and maybe even an old PC or tablet lying around - if you don't need remote access you could easily set up a separate network for cameras and DVR?
Yes and that's advisable (you'd be amazed what you can do with Raspberry Pi in this field). I like to put them in hardwired to a computer in a mechanical room or attic...
The problem remains the same. If the intruder is aware that there is a security system, and does not see a locally recognized security sticker on the door, he'll just take the computer, because it is likely that is where the data is stored, and you wind up with no proof.
Security requires off-site storage, or spoofing in hopes he won't discover the real system.
There are exceptions. One guy I know has his security system inside of his hardened storm shelter, which is a buried shipping container - Hard to find, and even harder to access... but that is a seriously unlikely circumstance for most folks.