Little lost designing a Network

So I'm designing a network for a final school assignment which I have to build, I've got a maximum of 3 32gb servers and 2 8gb servers to use in the network with 3 switches (+1 unmanaged piece of shit) and 2 routers. The switches will probably be Cisco 2960's

I've currently got it designed like this: https://i.imgur.com/HbpRpVI.png Some essential information here:

Blue = Management

Yellow = A network for other businesses to connect to

Red = Staff members

Green = Public Wi-Fi

Light blue = DMZ

Now for my concerns/doubts

1. The cables going out of the firewall (The colored mess) is supposed to be on 1 cable (So a VLAN mess) but I'm quite doubtfull it would work.

2. RDS is a function that has to work on the network, for it to be accessable from the internet on a 'safe' way atleast the gateway has to be in the DMZ if I'm right. Does that mean the staff users have to go all the way to the AD on one of the ESXi servers then go to the firewall to then connect to the gatway server for RDS on the DMZ and then somehow to broker has to direct the user to the RDSH which should not be in the DMZ? I'm just quite lost on the whole concept right now.

That's basically it, some feedback would be great to because I'm eighter doing something good or horribly wrong.

Thats basically it, I hope somebody can help me. I'm quite lost hahhaha