You asked:
1) Can I get 315 or 335s and remove the rear spacers?
2) Will both sizes give the same look I have now with wheels sticking out?
3) Which brand to go with? (assuming Mich or Pirelli)
1) You can mount wider tires on a 10.5" rim but it won't fit better than a 295/35-20 which is perfect fit. Are you going for looks or function? The wider tire size will look wide for the narrow rim and will bulge out a bit. You won't get much better street performance than picking a good street tire in the right size.
Michelin Pilot Sport 4S does not come in wider sizes that will fit 10.5" wide rim and match the front tire size of 285/35-20. Removing rear spacer will not help, only move the wheel closer to the inner suspension while an oversized tire will bulge on the rim.
2) Currently with your aggressive wheel offsets on OEM width rims and common spacer sizes you are about 5mm more poke on both front and rear than others on OEM rims and the usual 15mm front and 20mm rear spacers. Wider tire sizes will not look like what you have now, they may poke out more at the tire if you use your current spacers.
3) For street use, Michelin Pilot Sport 4S is the tire to have, others are just trying to catch up. 285/35-20 front and 295/35-20 rear will be fine and work well. You can find wider tires for the rear but might have to adjust front tire size and use tire diameters that are not OEM 28". You did not mention if you are on OEM suspension or are lowered. Any tire diameters that are larger than 28" will have issues with clearance if you are lowered and not running lots of negative camber (but this will wear your tires fast for street use). Continentals and Pirellis do make alternative tires and sizes that might work however none will have the comfort, low noise, good handling and performance in dry or wet and as long tread life as the 4S.