Here goes. I am NOT an organic chemist so please obtain other sources for information; i.e., don't take my work as gospel.

Question

a) I believe the second one you list is more reactive because the first one is sterically hindered due to the isopropyl group. And bromine is a huge molecule, also, which means it will have extra trouble adding into the double bond. (As a funny story here, when I was in graduate school and I took organic---many, many years ago---if the question of something not reacting came up we automatically answered steric hindrance and looked for the methyl groups.:-).

For b), I am going with two as the more reactive. The oxygen is an electron withdrawing element (it has a relatively high electronegativity) and it is closer to the C=C carbons, therefore, it will have more of an effect on the C=C bond and weaken it more than will the O atom placed 1 carbon further away. And a weaker bond translates into more reactive.
Check my thinking. Check with other resources. I hope this helps.

I thought this had to do with s-character which would cause stronger bonds but it looks like the pi bonded Cs all have the same s-character.

If these were acids we could try to find which was a stronger acid and conjugate base.

Would be nice to know more about these questions. At least I might know where to look or whether I've had the information yet.

I have to go to sleep now as I've had a long day. Looks like the organic people are going to be trying you this term.

Sheryl