Up until now I've been used to using my thumb for the lower 3 strings and then my 1st, 2nd and 3rd fingers for the higher 3 strings. I've begun learning a new song which has chords that span over the middle four strings, and so if I decide to pluck the chord with my fingers I'll end up using my first finger on the d string etc.

I'm just wondering whether its normal practice to use your fingers on the lower strings or whether strictly speaking I should be trying to keep my first 3 fingers on the g,b and high e strings.
If your doing blues then it doesnt really matter because sometimes NOT playing one part of a chord or progression may make it sound even better to you
Hmm well this track is a transcription of amazing grace so I assume I should use the method up until now where I strum the chords with my thumb instead of plucking them with all my fingers?
I try to keep my fingers on that "home row" as much as possible, but I do make deviations as necessary. The main idea behind this is just to make your playing easier and more fluid. Experiment with different combinations of fingers and strings and try to analyze which ones are helping you and which ones are hurting you.
Well trained players are able to play any string from 1 through 6, using any of the index, middle or ring fingers; similarly the thumb can play any string it chooses to. It is totally dependent on the musical context and what you wish to achieve.
honestly, i love and am stupid good at fingerstyle. its definately my thing. and i use whatever fingers work. dont play your fingers in a fist with your thumb sticking out and then call that fingerstyle, that's "i forgot my pick". if it is natural and it sounds the way it should, thats all you need kid. a good tip on this though is dont literally assign any fingers to any specific string. what works, works.