firstly welcome and congratulations on getting motivated to get into AG brewing, hopefully you'll find it very simple to achieve but quite rewarding, I know I did! Some excellent questions too!
To clarify, for this method where the wort is boiled and then chilled in the kettle, it should be a mixture of hops debris plus hot and cold break that settles in the bottom of the kettle as it cools. The Electric BIAB method
as a feature in its design filters out the hops material (in a hops sock) and some of the break settles in the urn. You can use a hops sock with MiniBIAB however we have skipped it here in the interests of simplicity (but I don't use one anyway, we'll cover exactly why in a later guide).
Basically, the light- brown flecks of muck are a mixture of (I think) hot break which forms during the boil process (which forms, gets broken up and re-aggregates) and also cold break which precipitates throughout the cooling process. Much of the hot break aggregates during the heating and boiling, so your boil is quite soupy- looking even from the beginning, then after the boil is finished and cooling starts, material continues to precipitate as the wort is chilled and that is cold break. (Chill haze is essentially cold break which forms only at lower temperatures, but not the issue here.) So, by the time your wort is cooled to pitching temperature, various break fractions have precipitated, but because we have yet to filter out hops debris, the crud at the bottom of the kettle contains that as well.
Conventional wisdom is that the more of these different break materials and hops debris we exclude from the fermenter the better, although there are differing opinions as to just how bad each of these things really are. I've tried to be slightly cautious and conservative in formulating this guide and catered for the school of thought that says all of them are bad for your beer and make your toes/ old feller drop off/ will kill you/ whatever, but we also want to get more than half of the wort out of the kettle and into the fermenter, because the when you're pouring it out, the first of these baddies will show up only about half way though. But we persevere and because we have a sieve and we can pour the majority of the wort through and still catch quite a lot of the undesirable material, but too much will just overflow your sieve.
Now, you can filter the last bit of really mucky wort that you don't pour directly into the fermenter through the sieve, the reason I don't add this left over fraction to the fermenter is that it isn't likely to be sterile* any longer once it has been filtered, unless you either filter it with a sterile filter and handling process or re- boil it, although you could then add it to the fermenter if you so desire, but bear in mind 'conventional wisdom'.
So, when I filter what is largely just horrible muck from the bottom of the kettle, I have a particular purpose in mind, and I use a cone of filter material which is designed for rejuvenating cooking oil, but voile would probably work well enough, maybe with a few layers in a funnel, cheesecloth might work too. I don't add it to the fermenter, I actually need that bit of extra liquid (usually a litre or so) for starter wort, I dilute it to about 1.040, add yeast nutrient and put it into lab style glass Schott bottles
which can handle repeated boiling and cooling cycles (so not just everyday glass bottles). It needs to be boiled before storage, then I utilise this to propagate and then 'park' liquid yeasts in the fridge.
Hope this helps!
* When I use the term sterile in this home brewing context, it isn't quite accurate as what I am describing is really just 'sanitary', but at these scales and conditions it is effectively sterile. A technical sterility requires higher temperatures and pressure to achieve.