Welcome to AF!
Tell us about the car. Year, miles, how many owners, any modifications, manual or automatic, etc. As always, the more info you can give, the more likely someone can help you with a useful answer.
Could the accelerating down hills be a cruise control issue?
Sounds like your brake rotors are getting wet- but it shouldn't take several pumps to dry them before they grab normally.
Definitely get any warranty work done while you still have the option.