No1. With respect to letting your base dry for 2 days before top coating can be a problem as well. Flash times are important but to much flash can give you similar results as not enough flash time. Most major paint manufacturer's recommend clearing base coat with 24 hours of basing and maintaining a temperature of about 70 degree...If your temperature is warmer it would need to be cleared sooner. 2 days may be to much flash time and clear coat adhesion may be a problem down the road. There are so many variables as to how much base you but on will also affect the recoatability time....check your tech sheets.
No.2 Allow more flash time between coats of base...make sure that solvents have evaporated, especially if you have a low hiding color and need multipul coats of base for coverage...pounding base on to get coverage is a recipe for disaster and as BarryK mentioned, solvents coming out of improperly flashed base coat can and will cause your clear to die off or give you that hazy look.
No3. How much air flow have you got in the area that your painting in? To little air flow will cause your base to not flash properly in the manufacturer's recommended times...To much air flow will cause your base to appear to be flashed off when only the top has flashed and the solvents are still trapped underneath and will come out over a period of time after you have cleared the car and have cut and buffed it...you can also have a delamination problem with improperly flashed base coats, when the solvents in the base try to escape, they often take the cured clear with it.
So to answer your questions...lighter coats of base, more flash time between coats of base, make sure your air flow is proper and check your tech sheets for maximum recoatability times.
Hope this helps.