Steven Zahm@ Jim
re: all of their social account links
There is already a repeatable field for social media links :)
re: Is it possible to add more fields and informational tabs
Yes, it is possible to add custom metaboxes and meta fields within them. Add them does require knowledge of PHP or require a dev to add them.
re: is there any coding limitations on the number of new fields and new field types Connections allows
No, there is not.
re: or supports in its plugin?
Connections has builtin support for all the most common field types. And, custom field types can be added quite easily. One such example of a custom field type is the Hours extension.
re: Are there any geniuses out there who can accomplish some customization cost-effectively to upgrade the Connections plugin to add far more fields and several more information tabs?
I’m nowhere near a genius, but I do offer custom development services if you are interested.