That wire is for an aftermarket amplifier for the radio... it can be removed if the amp has been removed, or you can keep it if you wish to keep the amp. I would highly recommend moving it though, that's a really bad place for it.
The control arms wear out just line any other suspension component. Fortunately, these cars have really simple suspension setups. To keep it relatively cheap, I would recommend replacing both front control arms, the struts (as well as OEM strut mounts and spring seats), and the rear shocks if those are also worn out.
These cars don't rust in any area in particular and are not known for rust problems, but like any other car CAN rust. Just take a look over the chassis. If it hasn't lived much of its life near the coast or salt, it's probably fine.
Basic things to check on these cars are the PCV system and the timing belt (particularly the tensioner and idler, as well as the water pump). If those things don't have a record of being replaced, I would recommend replacing them ASAP. The PCV being clogged up can cause seals to pop out (like the rear main) and lose oil, causing catastrophic failure.
If the timing belt or any associated pulley fails, valve damage is inevitable which is WAY more expensive than just servicing the timing belt. Those typically need replacement every 10 years/100k miles. Again, if no record is available, just replace that as soon as you're able.
Other than that, these are solid, reliable cars when maintained. Especially the 1998 models. I definitely suggest reading around on this forum and others (like Matthews Volvo Site and Swedespeed) for more info on the P80 cars and absorbing as much info as you can. They're actually pretty easy cars to learn. Good luck!