For 19b), the answer should be approximately 5.92 x 10^(-8) seconds.
In the solutions you attached, it seems that they thought v = 0, as opposed to v = u (in opposite directions, however).
If you go by their logic, they simply found the time taken to max height, which is half the time of the full flight (which is consistent with their working), as opposed to finding full time of flight.
As for 27c), the given diagram is a solar cell, and that's the what the question refers to as well. The photoelectric effect occurs in both photo cells and solar cells.
For solar cells, a current is produced through the photoelectric effect and as you've noted, there is a potential difference at the PN junction - when I was talking to the former head marker for Physics, he was saying how you probably don't have to go in depth with the PN junction forward/reverse bias etc.
In my opinion, the question is asking you to state the photoelectric effect and how electrons in the p-layer are excited from the valence to the conduction band. You probably need to make note of how the current is supplied for the load as well, as that is in the diagram. Sorry I'm a bit rusty on Physics, so I'd love if someone else could further expand on that question!
As for 29a) no clue don't do medical phys