Wiring a Heater, Vent Fan, Light for bathroom
Hard to tell from the pictures what you currently have. But here is (roughly) what you need.
Updating based on newly posted installation diagram
Assumptions

Installing 3 switches in one box Note: I do not know much about how much you can stuff in a box. There are some experts here who can speak to that - when I did this in my own house, my electrician dealt with those details (and many more). I got something like this Decora 15 Amp 3-Rocker Switch which can fit in a single gang box, but be warned that a single gang box is likely not big enough for all these wires (code or practically speaking).
Everything on one circuit - i.e., a single 15A or 20A circuit as appropriate based on the requirements of the fan/light/heater - primarily the heater is the determining factor

In the switch box:

Cable 1: From the main panel: Black (hot), white (neutral), ground. Hot goes to all three switches. Neutral will connect to neutral from all three devices.
Cables 2 &amp; 3: To the devices: Typically 2 cables. One black/white/ground (this is the /2 - 2 wires + ground), one black/red/white/ground (this is the /3 - 3 wires + ground). (Technically this could be done with one bigger cable or with 3 black/white/ground cables or with a bunch of individual wires in conduit, but it looks like you have the typical 2 cables already, so that's good).
Connect all the neutral (white) wires together with a wire nut.
If your switches have three pairs of screws then connect three short black wires (same size, easiest to just strip a section of Romex and chop off 3 pieces of black wire) together with the black wire from the panel with a wire nut and connect each to one screw. If your switch has a common hot then you connect the hot from the panel directly to it.
Connect each colored wire from the cables 2 &amp; 3 to a switch. Two switches get black, one gets red - these are all switched hots.
All grounds are connected together.

No white wires to the switch unless it is a smart switch that uses neutral
If your switch has backstab connections and screws always use the screws.
At the fan:

Connect the neutrals for the light &amp; fan (whites that are paired with the blue &amp; black wires) to the white in the /3 cable.
Connect the neutral for the heat (white that is paired with the red wire) to the white in the /2 cable.
Connect the black (fan) wire to the black wire in the /3 cable.
Connect the blue (light) wire to the red wire in the /3 cable.
Connect the red (heat) wire to the black wire in the /2 cable.
Connect all grounds together (as always)

Color-coding: Because the heat uses a lot more power than the light &amp; fan, it gets the /2 cable. Harper recommends (and it is a good idea) marking both ends of the /2 black --&gt; red and both ends of the /3 red --&gt; blue. That will make all the wire colors match, which will help with any future troubleshooting. However, you must make sure that the whites go to the correct (/2 for heat, /3 for fan &amp; light) whites - neutrals &amp; hots must be matched together.
That should leave you with nothing extra hanging out. And you should have each switch operating a separate function in the fan/light/heater.
You also need to vent the fan properly. I had my electrician do that too (not a fun job in my attic). You definitely do NOT want the fan venting into the open area of your attic. If you had another fan before then you may be able to reuse the ductwork and the hole in the roof. If not, that may be the hardest part of the job.