Can I strengthen my eyes by doing exercises, like repetitively looking at close objects?
No. Exercising muscles of the eye improve neither their ability to focus nor to move from side to side. This might seem counterintuitive since all other muscles of the body can be made to improve their performance by exercise, but the muscles of the eye are different in this regard. The difference might partly result from the fact that the brain provides very precise control for eye position and exercising the muscles does not influence the signals coming from the eye to the brain.