My toddler likes to play with himself -- is that normal?

VERY. This is very normal and not worrisome. Children will explore all parts of their bodies and touching is a normal part of that. Try not to make a big deal out of this as this may elicit MORE of the behavior. Teach children that there is a time and place and that this behavior should only be done in private and without exposure to strangers or other kids.
Yes. Masturbation is ok for this age. Nothing to worry about. Just redirect him and no discipline or scolding for this.