My boys are 20 months apart. Some survival tactics for all of us, and answers to your questions:
I never used a sling to breastfeed with (I never figured out how that would work) but I developed some pretty good arm muscles and just learned to clutch the baby really well and breastfeeding while moving around--I can even mop a floor breastfeeding. :) (They didn't think it would qualify for the church talent show, though.)
Any chance you get--even if the weather is overcast and a bit yucky, toss rain boots on your toddler and get out with the sling. If you have a double stroller, or a regular stroller and the sling, that has a decent cover on it to block a light drizzle, get out for the fresh air (just keep your head covered, too). Once you're cleared to start exercising again, find some fun workouts you can do with minimal equipment in your living room. We have very little indoor space, but my older boy LOVED to exercise with mommy and used to even watch the workouts when I wasn't doing them and try to follow them himself.
If your toddler has a special doll, encourage her to take care of her baby while you are taking care of your baby (feed, change, burp, snuggle, etc.) then snuggle your toddler when you're finished caring for the baby.
It was a little (or maybe a lot) bumpy at first with them so close together, but it got better and now my 4-year-old and 2 1/2-year-old are happily waiting for their new baby brother (5 more weeks???). See if you can find any other moms with children their ages in your area to meet up with--even a change of living room can be a big help!