I'm an offsite guy, so I'd chose the first option every single time. I'd never stay on property. I couldn't imagine WDW without a car, it gives SO much flexibility and convenience.
As for crowds and heat, literally impossible to know. Generally speaking, May isn't the busiest time for WDW, but nobody can predict if one week will be busier than another (barring a major event like spring break). For weather, just like anywhere else in the country, it's impossible to predict weather more than a few days out. They could have a heat wave one of those weeks and it'll be in the 90s. They could have a cold snap and it'll be in the 60s. You won't know for sure until a few days before you go....regardless of when. Generally speaking the "peak" of summer is late July, so temps on average get warmer until then.
