I see...
I'm also new here...
You will use 3 switches, why didn't use only 1 switch?
Isn't it stopwatch right?
So, I think 1 switch is enough for start/stop toggle mode.
or maybe two switches, the other one used for hold the timer...
For the 8052, use its timer maybe the easiest way. For using it with nearly exact to real timer, use crystal with 10.xxxx MHz value.
for the output, LCD M1632 can be used, or if you want to, u can used scanning display for 6 seven segment displays.