Well, the reason why your walls are all textured is because texture helps hide minor defects in the drywalling. If the walls weren't textured, it would be easier to see what the underlying problem is. Often wall studs will twist and split as they dry out from a supposedly "kiln dried" condition, and these changes to the lumber as it dries may cause problems in trying to get the drywall nice and smooth and flat. And, if you can't get it smooth and flat, you can always apply texture over everything so that you can't see that it isn't smooth and flat.
However, if there was any damage going on from a roof leak, you'd see dark areas on the ceiling where it was wet, and I don't see anything like water damage on the ceiling anywhere.
What you should do is talk to the person who sold the house and ask if he or a contractor did the texturing. Find out how the texturing was done because the hardest thing to do when it comes to any wall or ceiling repairs is often matching the texture of the surrounding wall. You want to find out how it was done so that if you ever do any repairs, you'll know how to match the texture of the surrounding wall for an invisible repair.
I really can't see any bulges on the ceiling, but I presume that the existance of a shadow near the wall indicates that the ceiling isn't flat. I think much of that is simply due to the fact that the light source is close to the ceiling, and is perhaps exagerating the "unflatness" of the ceiling.
Those lines across the ceiling in the last photo look to me like cracks in the texture over joints between drywall panels that weren't taped. The whole idea behind drywall tape is to carry any tensile force across the joint so you don't get the joint compound breaking if there is any tension in a wall or ceiling. The tensile forces would come from the wall or ceiling bending a little. If you have someone slam a door so that the increase in air pressure inside the room applies over the whole wall and causes it to bend outward a bit, the convex side of the wall will have to stretch a little, and that's where the drywall tape come in to carry that tension so that the joint compound doesn't crack. Similariliy, on a ceiling, if someone is walking on the ceiling joists in the attic, then the bending of the joists can cause the ceiling to be in tension. The drywall tape at the drywall joists is meant to carry that tension across the joint so that the joint compound doesn't break.
I suspect that whomever did that drywalling simply didn't tape the joints where you see those straight cracks. You could repair that by using a paint scraper to scrape off the texture on either side of that crack for 2 inches (say), taping the joint, and then applying texture over the tape. However, to match the surrounding wall for an invisible repair, you'd have to know how they textured the wall so that you can make your texture look the same.
Personally, I don't see anything serious here, and if I were you, I'd learn to drywall and plaster with easier projects than these. From what I can see, these bulges and cracks aren't very serious and don't indicate any serious problems with the house; they're just cosmetic. The cracks in the ceiling may get longer and join up, but I don't see why any bulges would get bigger. So, if it were me, I would just leave them until you get enough experience drywalling that you feel confident in tackling these issues.