Walking is great. There is also something called stroller aerobics that a lot of new moms find helpful. See if there is a class near you check with the local hospitals to see if they know of classes. Also google kegel exercises. Can also talk with karen quigley at trueformcoaching. Com. She's very good in this area & does online personal coaching.
Varies. After c-section, no lifting above 10 lbs for 6 wks, but can exercise similar after vaginal delivery other wise. Take exercising slow since there will be in a shift in postural balance due to a rapid weight change after delivery, other then that, you can start any exercise program that is appealing to you and one that you can stick to.