For the correct rezising:
If you want the textblock from changing its size, when the group is rezised, you have to look at the formulas of the width and height.
If they are sth. like Sheet.123!Width*0.43 they rezise when Sheet.123 (the group) rezises. You have to use direct values, like for example: 34 mm.
If you than use the GUARD function on top of it, nothing should happen to the textblock anymore, so for the width cell: =GUARD(34mm).
ObjType 2/10: Using 2 the Group becomes an outomatic connector and takes part at the automatic routing routines from Visio. Using 10=2+8 you allow the members of the group to take part in the routing, too, if they themselves have the value set to 2.
For the connection points:
When you made the group a connector, it got the green (in Visio2010 blue?) points that represent Begin and End of the Connector. Those points can glue (=connect) to other shapes. But they are not connection points themselves, that means other shapes can't connect to them. Normally that is not neccessary, because the connector should connect to sth. not the other way round.
My suggestion ot adding two connection points near beginning and end had another background: You could analyse then, if they have the same x or y coordinates like the Begin (or end) and so you know, if that end is horizonntal or vertical and can use that info to psition your textblock accordingly, and that is your main problem, like you said yourself.