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.