Positive measure of a Lebesgue measurable set

Question

Here E is a Lebesgue measurable set in $R$. Show if the following is true or false:

1. Every uncountable measurable sets must have positive measure.
2. Every set with positive outer measure is Lebesgue measurable.

Can someone please answer this. I am not sure if uncountable sets are measurable or not. Also, can the outer measure be negative in the case of part 1?. I know if m*(E)=0 then E is measurable so does that mean part 2 is false? I am mixing up these two cases so can someone please answer them?