I’ve heard it used – and used it myself – in America to mean ‘I need to make some sort of pleasant noise here even though I don’t actually like the thing very much.’ Think, ‘Oh, that’s nice’.
I’ve also used ‘Nice!’, and heard it used, to mean ‘That’s a really neat thing/accomplishment!’
Some of it’s in the tone of voice; but some of it is just plain confusing. Which is why one can get away with using it for ‘I don’t think much of that but I need to say something good about it for social reasons’ – because whoever you say it to can’t be entirely sure that you didn’t really mean to say it’s good.
– in the OP post, I would take “quite a lot” to be more money than “rather a lot”.
In those contexts, I’d expect exactly those same meanings in current American English.
From the preface of a book of comedy scripts by Stephen Fry and Hugh Laurie:
The authors would like to make public their immense feelings of gratitude towards Roger Ordish, Nick Symons and Jon Canter who produced, produced and script-edited “A Bit of Fry & Laurie” Series 2 respectively. It would be no exaggeration to say that their contributions towards the programme were quite useful.
I think this is the key. Literally, they are merely intensifiers, like “very,” but depending on context, especially tone of voice, they can mean something else.