Rests not going away

Yes, start with voice 1 in every staff.

Always start with voice 1 in every staff. If you need another voice use voice 2 so all voice 1 stems point up and voice 2 point down by default. If you still need more voices add voice 3 if you want stems up and voice 4 if you want stem down.

When it comes to cross-staff notation see https://musescore.org/en/handbook/cross-staff-notation for more info on how to do that. If you need 5 voices in the bass clef you'll need to put one in the treble and use cross-staff. Outside of some rare fugues there is never a need to use more than 5 voices on a staff and never a need for more than 8 voices total between the two staves. I've seen 4 staff piano music and there are still not more than 8 voices total in this music. The only case I've seen more is when there is a pedal staff for an organ and that staff is notated for the feet.

As mentioned, you do indeed want to start with voice 1 on every staff, and you can use cross-staff notation where desired if a single logical voice needs to move from staff to staff.

I've never dealt with a six voice fugue - at least, not on only two staves (I've written large fugues for ensembles). But it wouldn't come close to taxing MuseScore's abilities. Three voices for the top staff, three for the bottom, with cross staff notation as required, and you still have a voice to spare on each staff. You could do an eighth-voice fugue on two saves if you really wanted.

FWIW, this same basic model is how almost all notation software is organized.