You could do most of that list with an iPad & a USB/Lightning interface, these days... or any computer.
GearRank - The Best iPad Audio Interfaces has a list of current offerings, with reviews.
There is also software, free & paid, for recording. Just as an example, see http://www.ikmultimedia.com & look at the drop-menu links for Products > ...
From the description, I'd say that the mixer qx1002 model which I also own
You can connect the macbook via usb and send the signal to mains by pressing th button labled USB/2tr to Main Mix, alternativly the signal can be send to phones only
Note that the mixer only has two preamps - so if you're pluging in acoustic guitars or microphones without external ...
A mixer will have multiple channels for your multiple inputs.
Each channel will have a trim pot (gain knob) for adjusting the input level.
(Sidenote: some channels may not have a trim, those are line-level inputs, not mic-level inputs, and they are meant for things that already at "line-level")
You set your gain as you need to for each channel, nothing ...
The use of a field mixer is not restricted to mixing several sources into one track. It is often used to send individual sources to individual tracks.
When you need to mix several sources into one track in a live dialogue recording situation, you have to dynamically deal with each of the sources as the shot goes by. Having sevral microphones continuously ...
If the bass is lacking, then it sounds like there's a phase issue, i.e. a false connection or bleeding of channels. Quite unexpected though and not something I'd consider a feature of "a bad quality mixer".
Curious, this type of mixer is sturdy and doesn't start acting up suddenly (in my experience at least).
What do you mean with 'tails' is that the multipin output on your mixer, with the screw on plug? If so, have you tested the XLR outputs? How do they sound? Also can you listen to both outputs without the SD702 in between?
Depending on the length of documentary and your future needs for recording equipment, I would suggest you to rentthe gear. Although it is very tempting to buy gear. If you are not experienced yet with using field recorders and different mic's, why take the risk?
5000 dollars is a lot of money, which you could also save up and spent on 2nd hand ...