1) If we're talking about custom parts, I think you've got enough to build quite a few machines. I'd say at least 8 different machines with differents parts. But if we talk about other non-custom machines, you can try out Deep Claw, which is somewhat similar to Blue Falcon, but with higher grip and slightly higher booster. Just slightly.
2) I've seen you commenting on another thread that made mentions of Quick-Turning, so I'm assuming you're gonna try to go with that. One body part that I'd recommend when starting out is the Sky Horse, coupled with the highest ranked cockpit part you have available (Super Lynx or Combat Cannon for example), as well as a B-rated booster like Titan-G4, Meteor-RR, or the A-booster Triple-Z. If you don't mind very low acceleration, Thunderbolt-V2 and Devilfish-RX are available for you, as well.
3) It's been a while since I played Grand Prix mode. But I think I went with Space Angler last time (a light but slow machine with weird strafing ability). If not, then Deep Claw or Hyper Speeder.
4) If we take away custom machines, Blue Falcon does pretty well, surprisingly. It may be a starting machine, but it can do most of the advanced techniques with decent results (at one point, it had the non-custom World Record on Cosmo Terminal Trident). This spreadsheet has all the non-custom machines's times registered, to give you a small idea of how these machines are played at very high level : https://docs.google.com/spreadsheets/d/17DqpOEgzh0RqSKZ-5q5kanhI3uRhQ6w0xo4GTJO5cQI/edit#gid=0
But Blue Falcon pales when you compare it to most custom machines.
5) I'm playing using a controller, but because my control stick is broken, I need to use the D-Pad instead... And I've been playing this game for quite a few years with this setting, and I got so used to this configuration that I can't go back. XD Also I go with the third person view (there are 3 third person views : default, 1 rank further behind, and furthest camera setting. I'm going with only 1 rank behind, and so does most players, as it gives a better view of what's happening around while not taking away the "wow i'm going so fast" feel.) The only problem with first person view is that without much information on your surroundings, you might take corners too tight. But it's like me when using the D-Pad : if it works for you, keep on going !
I know F-Zero AX Arcade Cabinets have a steering wheel, and in the GX manual there is a mention of the steering wheel option, but that's the first time I've heard of anyone playing regular GX with an actual steering wheel.