Regarding the Romana thing, it seems clear in her second incarnation-at least in her debut season-that she's intended to be sort of a female Doctor (well at least the fourth one). In "Destiny" she briefly wears Tom's getup, and the pink outfit with white scarf she wears for the rest of that serial is pretty much the same idea.
I'm pretty sure she has her own sonic screwdriver as well.
Yes, in Horn of the Nimon
, The Doctor hands her his Sonic Screwdriver, and she shows him she made her own. Then he tries to pocket Romana's and give her his, LOL.
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?