Yes and no. If you bypass the bose amp you lose the door subs, so any gains in mid/highs won't sound as good.

Run new speaker wire from HU to new speakers if using internal radio amp. Or run RCA's from HU to new amp, then new speaker wire to new speakers and sub.

Depends on the amp you go with. If you just change HU/speakers (keeping the door subs), many have used Polk db351 & db521 or Boston Acoustics S35 & S55.

If you go with an aftermarket amp and add your own sub the best combo is 6.5" components in the doors and a sub in the trunk.

That depends on your budget.

Not counting the HU, you can make it sound noticeably better with just the twiddler replacement for under $200. Add a budget 4-channel amp going to 6.5 door components and a DIY sub box, easily possible for under $500, sounds much better but won't come close to a quality system. For about $1000 you can get a pretty good sounding system with a nice 5-channel amp (Dennis has XR-5S around $400), some quality components, coax rears, and a pre-made sub/box for the rear.

You really need to come up with a budget first. Figure out if you want to replace door subs with aftermarket. If doing new sub can you DIY the box. Once you have the guidelines figured out just throw in the best equipment your budget allows for.

If tearing the entire interior out of your car doesn't scare you, and you can swing an extra $150-200, soundproofing materials from Rick at RAAM audio will make even the stock system sound better