Is there? and if there is and if you reach it will you still be able to save your game or play it?
Yes there is a 999:59 limit though I don't know if you can't play after that. I think you can but it just won't count the time and if you save then it always saves at 999:59
No. You can play the as long as you want. However, Pokémon games for the Gameboy Consoles do run out when the internal battery has run dry, rendering it un-savable until you re-place the internal battery
On the screen, yes. 999:59. But you can play over that time, but the time will not be added.
There is not max time. You can play forever. On my game on the startit says
>play time: 999:99