Basketz the BoreofWhabylon (great name) has it, it's a T12-L1 region injury leading to paralysis below the hip line, and complete incontinence. Of course there's always the Ambridge Health Fairy, but in real life, "a fragment of spine sticking into the spinal cord" is an incomplete spinal injury and is going to seriously mess with your anterior spinal column, so actually your chances of walking really functionally again and doing any form of actual farm work are basically nil.
With an amazingly good recovery of the "miracle" sort, you could potentially walk, but you'd have serious issues on unstable ground, let alone being more than 10 mins from a loo, and the constant and relatively unpredictable pain, general neuromodulated problems in lower pelvis/limbs, etc. I have known one person recover from this kind of injury, be able to XC ski but not walk well with poles, live life catheterized, and seriously consider doing a long-distance low-temp ski trip with Help for Heroes. He ended up not doing it due to bladder/bowel issues that were just too insurmountable. THat's the really horrible thing about spinal injuries - it's the little daily bastarding things that wreck your life forever, once all the hard work of rehab is over.
The chest injury is presumably broken ribs -> pneumothorax - as i said above - likely to be less of a problem. But a high risk, particularly in previous heart attack patient, of dying of something like an aortic dissection when there is any extra strain.