In need of a hand with a working prototype

Hi there,
I’m in need of some help! I’m currently studying industrial design at uni, and with one of my assessments I’m developing a working prototype. I’m not getting marked on my programming skills or how I assemble my electronics aspect but my prototype must work. Basically I’m developing a system that combines the features of a repetition counter and a stopwatch. I’ve had no prior experience with programming or Arduinos and I’ve been thoroughly thrown in the deep end not knowing anything about code or electronics (it’s not really part of my course, nor is it taught in my course, however I do need to develop a working prototype). I was hoping that maybe someone could lend me a hand and help me what I need.

What I need to be able to do is to program my Arduino mega board to have two functions once the device is turned on through a switch. One that acts as a counter in intervals of 01 up to 99 on 2 1 digit 7 segment displays. And the other a minute:second (00:00) timer on a 4 digit 7 segment display.
Basically I designed my idea to have two buttons to switch between the two modes (so when one mode is on the other is off). Once the mode is selected, there is a central button that either starts the timer or counts up 01 when pressed. Both modes use the same central button. When the button is pressed again it either stops the timer or adds to the count (so it would show 02 now). The two buttons for mode selection would also act as reset buttons when pressed. I’ve drawn a diagram that I think sort of explains it a bit better.
I’m really just looking for some help as to where to start or if there is some existing codes and wiring displays that I can adapt my idea to. As I’ve said, I’ve never used Arduino or coding before and with only a short time frame of 5 weeks till the final assessment is due I feel that I need the help of someone to help me walk through this process. Hopefully some of this makes sense. Thank you to anyone who gives me hand in advance! Also hope this is the right place to ask this sort of question.

I'd suggest that you get an Arduino Starter Kit, for your first steps into wiring and coding, and for building your prototype. Begin with understanding the use of buttons and switches. The next step is adding the displays, which can be driven by decoder chips or by shift registers, in a static or multiplexed way. You'll find a bunch of 7 segment and LED matrix projects in the forum or web. Perhaps it's expected that you drive the 2 digit displays by decoders, and the 4 digit display in multiplex. In either case you need some peripheral chips to drive the displays, because the Arduino does not have enough I/O pins to drive the segments directly, and the 4 digit display most probably requires multiplexing.

To make things easier for an beginner, search for available display modules which come with Arduino libraries and/or example code.

Because you need to drive a large number of LED outputs, a dedicated LED driver chip might be useful. I expect that there are a number of 7-segment display modules available for purchase with the chip already on board. Look for ones that claim to only use a small number of Arduino output pins.

I've used the MAX6971 in a couple of projects to drive discrete LEDs. It's very easy to use with a large number of LEDs because it does the hard work of controlling the current through individual strings of LEDs. It's also available in a through-hole version so you can put it on a breadboard.

MAX7219 is good for discrete LEDs also, very easy to use for up to 64 LEDs.
Set up 5 registers in setup(), then write to 1 of 8 data registers to control LEDs. each register controls 8 LEDs.

I've been thoroughly thrown in the deep end not knowing anything about code or electronics (it's not really part of my course, nor is it taught in my course, however I do need to develop a working prototype)

Is "hiring a team to do the work" part of the course?