Ok, lots of stuff to cover.

I'd honestly say go with the Prusa I3.
It has a large following making instructions and help easy to find.
It has many different models to choose from, including dual extruders.
The frame is easy to make from scratch out if almost any material.
Fully assembled, full kits, and partial kits are available. Most of these are laid out in detail, there is your parts list with dimensions.
They also tend to be low cost.

Ok to answer your questions I quoted:
1. I would say that if you wanted to have pellet to filament converter directly into the printer you should give yourself a lot more time. Of you where making something like the Filastruder, you might take up your entire deadline to get a constant product. So that portion may be a little too ambitious. As far as using nylon thread directly into the printer you run into a lot of problems. One being heat, nylon tends to have a higher melting point than ABS so you'll need an all metal hotend like the E3D V6. Then there is the diameter and structure of the thread. Braided thread is very thin. If you where printing with a 0.1mm or 0.2mm nozzle, then thread might be able to displace your melting chamber enough to extrude the nylon, but then you run into the structure problem. Being braided means it likes to crush when pushed together and stretch when pulled, this would cause your retraction settings to have to be greatly increased and thus slowing down your print speed by a large amount and possibly causing consistency issues. If you could get all that under control you'd then have to deal with the material itself. Is that nylon meant for thermoplastic reheating and extrusion or will it just melt, burn, and turn into a brittle mass?

2. A heated bed is beneficial for controlling warp in prints caused by rapid and/or uneven cooling. While the amount of warp is different depending on material, it is suggested for all thermoplastics and is not dependent on what setup of FDM/FFF printer you use. If you're printing with PLA or some other low melting point thermoplastics than you might get away without one. Anything to 220°C or higher, like ABS, it is practically necessary if you want any degree if quality assurance.

3. Depends on what 3D parts you're trying to mill and the effort you're willing to put in. Most 3D printer specific models are so designed for their ability to be printed with intricate internal features that can't be done on a CNC mill. If you are adept at modeling though, you may be able to cut the models and edit them into separate, millable parts.

4. With the timetable and work you have to put in so far, I'd strongly suggest you buy an electronics kit, at least containing the processor, drivers, endstops, and steppers. This with the intension of buying one that can run off an SD card answering question 5 by saying if you can run it off an SD card, you can skip Octoprint and save yourself the time and money.

I know this is a lot and I hope it helps. If you have any more questions or need anything clarified don't hesitate to ask.

Ditto (I tried to give Karma for your answer ARKtest but apparently I have to spread my Karma around more).

If you have a fast approaching deadline then I would suggest that you make things as simple as possible for yourself. The 7th is just over a week away and within that time not only do you have to order the printer, put it together but also get it calibrated and running so that it can produce viable prints. With the time frame you have I would even suggest, if funds allow, removing the build phase and buy a ready made machine. You are going to need to reduce possible problems (not to say that you may not get these with a pre-assembled machine).

The other thing that you may want to consider is, if you are putting this together for the client, who is going to be using this machine once it is built. i.e. are you handing it over to them and they are to operate it or are you going to continue using it? If you are handing it over then it may need to be as easy to use as possible. Not everybody is a maker geek (that's a compliment rather than a derogatory term).

Don't underestimate how much work is involved in getting a printer up and running properly, even those that profess to being plug'n play 3D printers are not always that easy to set up.

If you want to go down the kit route then the Prusa i3 is a good format and has a lot of support. There is also the Huxley Duo Kit from RepRap Pro, the 12 month warranty that you get is not a bad thing.

Of course the other thing that is going to determine what printer you get is what you want to build, large or small, high detail or low detail.

I laughed for a good while, thanks dig.

@sheila Dig is, as always, spot on. Check out www.productchart.com and compare some of the fully assembled and full kit printers to help narrow your search down. The results from most of my comparisons and a lot of the requests for which printer to get are why Dig and I suggest the Prusa I3 as well as the Huxley.

welcome to the forum. Kepp us posted on how the project is going.

ARK, since Dig needs to "spread his karma around", allow me to fill in.

Lol jump in any time Chris no one can suffer from too much assistance on a forum.