1. Yes, in almost all cases. Insufficient oil temps prevent the fuel from evaporating and getting sucked out through PCV. 2. Injection pressures can cause fuel to leak past the combustion rings and contaminate the oil.
Interestingly, even on high diluters like the Ford EcoBoost engines, there have not been the catastrophic results predicted by people who are shouting from the rooftops about fuel dilution. It appears if you go by the OLM or sensible OCIs, fuel dilution is not the death sentence that old logic would have you believe.