Hi there. I had a son with some separation issues as well as being quite possessive of me. He didn't want daddy and he didn't want daddy hugging me! I would just say "no. We are nice to daddy" and hug daddy in front of him. Then we ignored it. If he got 'crazy' and was melting down or something, he got a time out as we had a 'no fits' rule.
The separation anxiety I never disciplined for because it was true anxiety that he was displaying. I found that if I did as you said, stay a bit and let him warm up--- then he'd be more comfortable.
I'm not sure I'd allow a 3 year old to take over my ipad. I would say "off limits" if he was trying to alter anything on it. Consequence of that is that the ipad goes away for X amount of time.
Are you away from him a fair amount or something? He does seem to have a bit more than your typical in terms of possessiveness of you.
Yes. Your son requires your discipline for these behaviors. Through appropriate discipline, your son will learn appropriate boundaries in terms of the appropriate ways to get your attention. If this behavior was generalized to others, then I would be really concerned about his esteem and need for attention and affection. However, this behavior appears to be more focused on you.
Only give him your attention (hugging, kissing, holding, talking, etc...) when he behaves appropriately. When you give him your attention when he acts out, this will only increase the inappropriate behavior.