This is fabulous Louise who is well on her way to her goals! The first picture is a pull-up, and you can use anything that is chest high - like a tree branch, playground equipment, etc.
Push ups with the hands elevated is slightly easier on the back, if there is weakness.
This exercise is great for cardio, if running is a problem. You can use any old piece of rope, but if you want it to last make sure it is thick, as you burn through them pretty quick! Basically you row as hard and fast as you can.
Below is a version of the woodchop, with a sandbag and an extra squat in the middle. You load the bag up onto your shoulder, squat, then unload it. It gives the back an extra bit of oomph and will get the heart rate sky high too!