Richie,
First of all if the ballad was written in about 1750, which is my guess taking various factors into account, the earliest extant text has still had a pretty long time in oral tradition to have picked up some misunderstandings/mishearings.

Then don't forget that one of the main characteristics of these ballads is the leaping and lingering that pays no heed to time gaps, so the death of the parent(s), the care (or perhaps fears) then the going overseas initially by the brothers, the trust in the apprentice, and him rising to the quite prestigious status of factor, could all have taken place over a considerable timespan, say several years. So at first the brothers go themselves to initiate the business, but then they decide to send a go-between.

I think you have a point in the brothers' displeasure on finding out what the daughter and the factor were up to. They had placed their trust in him, she wants to marry beneath her, she wants to share her wealth with him. Sufficient motive for those times. (Actually in some cultures this still is the case today even in the West).

It's worth a try putting 'factor' in the search box on the UCSB English Ballads website. You might at least come up with 'Turkey factor'. In the 18th century if you were sufficiently wealthy in Britain and there were many nouveau riche then, you would want to stay in your large mansion and let someone skilled in import/export do all your negotiating, travelling and money making, making you even richer.

'Bridgwater' is the modern spelling of the Somerset town, but there are other Bridgewaters in Britain, as there are many on your side. I don't think there can be any question now of which Bridgwater is intended.

I think 'bestow the same' here means her portion, not another £3,000.
The expression 'the same' in 18thc English actually means 'the aforementioned'. You've no doubt heard the expression 'the very same',meaning 'what you were just talking about'.