1. Is one required to have a license to fly planes?......I realize that for many of the larger, more powerful planes, it is logical.
At an AMA chartered club, you must have an AMA membership to fly there. You may fly a model airplane anywhere you wish, provided you have the landowner's permission and do not endanger anyone.

2. I only plan to fly electrics. For now, probably park models.....However, what determines a park model, from any other
There are no real criteria. "Park flyers" are generally under 24" wingspan, and modestly electrically powered.

3. At some point in time, I would like to build my own planes, from kits and maybe, my own design. Where does one find out what restrictions there or, regarding this.
The only two restrictions I know of in the USA are weight (55# or less), and turbines, which require a special license fo aly at any chartered club field.