On core strength:
Get down as though you were about to do a pushup. Lay your forearms on the floor. Make it so the bicep-arms are directly vertical from the ground. Then click your heals together and stand on your tiptoes as you normally would for a pushup. See how long you can keep this position. I belive this is called the 'bridge'.
Once you get good at it and can keep it for 50 seconds or so you can start doing pushups on a plank with a ball underneath. Need to be careful but then it will work both your arms and stomach core strength.
On Stretching:
After exercise one should stretch so as to prepare the muscles for next time. You should not stretch before you have done at least a warm-up exercise as muscles are more pliable when warmed up. You should not stretch joints, this can result in injury, joints cannot move any more than they are already capable, if you put pressure on them you are likely to damage it.
