I need some help, fitness reddit...

My info height - 5'7" weight - around ~200lbs (not sure, I don't own a scale) age - 28

I was in very good shape years ago. At my peak (19-20 years old) I was around 150 with defined abs, but not a full 6-pack, walked everywhere, huge legs and calves and good upper body and cardiovascular. However, I was angry, and motivated to workout til I dropped to burn off rage and keep myself out of trouble. Part of it was a very physical job, the rest DDR (hey, it works) and weight lifting. I fell off from the exercise routine maybe 6-7 years ago and never really got back on.

I've been trying to get in shape recently, and am having some issues. I've been primarily doing pushups, crunches, standing squats without weights, and burpees. I don't have any weights (except for 2 20lb dumbbells)

I'm having two problems, and I don't know what I'm doing wrong or if I'm overdoing it.

1. With the pushups, I'm finding I'm having serious problems with my left shoulder. I don't know if the problem is related to the pushups or not, but at some points it feels like I can't even do the pushups because of a sharp pain in my shoulder when I do the pushup. It's only on the left side. I should mention that I don't have a lot of flexibility in my shoulders, and they "pop" sometimes when I rotate them (my knees do the same thing when flexing them, I have some joint issues due to being born premature). I'm doing them on the floor at times, but mostly I've been using the Perfect Pushup. I'm wondering what people think of this item. I feel like I get a better pushup with it, and more of a workout, but also I noticed that doing pushups on the floor last night I didn't have shoulder pain, so wondering if I'm using it wrong or if it's just a bad device.

2. Burpees: I love them, but I'm hurting like hell from them. I feel like I'm really getting an all around workout. Not a real gym workout, but I can't really get any gym equipment right now as I'm moving long distance in a few months. The burpees are great and I can already feel a difference in strength and flexibility, and my big belly is starting to shrink, but twice now I think I've pulled something, pain in the lower abdomen and can't even do a single pushup. Both times this happened I couldn't really do anything for 3-4 days, and even then I could feel it. Is this a pulled muscle, like I overdid it, or is it normal? I went from couch potato to the pushups and burpees. I'm not very active normally, but am trying to do what I can at home. I'd like to jog and do more outdoor activities, but I don't live in a very good area, and outdoor stuff is out until I move, as is any gym membership.

Sorry for being so long winded, and any advice on what I'm doing wrong (or if this is normal for starting out with exercising) is appreciated.

TL;DR - pain during/after exercise, unsure if it's normal or I'm doing it wrong