Unless a patch of some sort is made that easily fixes the FPS cap, I don't think it should be allowed. As for widescreen patch, I think should be fine as it does not affect gameplay. A change in FPS does, as it could affect the timer as well as the cars' handling. We need to conduct tests to check for the effects it has on gameplay but runs done with 60fps will most definitely be better than 30fps. We could also have a 30fps/60fps sub-category for ILs.
Best hotlap would work best, regardless of how many laps.
Pretty sure installing it to an SSD is fine, I don't see it being banned from use in any modern (PC anyway) game. The other two I think wouldn't be allowed as it's a modification of the game and FPS changes can probably affect the game's physics as is the case with many games from that era.
Here are the tracks:
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Japan Split Decision Full Impact Bridge Banzai Divine Reflex Burnzilla
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Germany Lethal Rush Vertigo Ridge Terminal Descent Switchback Blast The Bobslayer
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Italy Gladiator's Shadow Nitrous Maximus Decimation Legion's Climb
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USA Airtrauma Bayside Hustle Fear & Rage Chinese Burn Airtrauma: The Revenge San Frantic
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UK Blitz Assault Exit Pressure Riverside Dash The Ripper Knight's Rampage
Reputation doesn't seem to affect anything as you unlock DVDs depending your car's star rating and you unlock parts after a certain amount of races.