If functions and Conditional formatting

Hi
I have two issues with this workbook.
I’m having problems with columns E and F with the If Functions.
I would like the cells in E and F to return the formula value only if there is a value returned in the cells under column G, which does not fill after the end date (Cell B10). For Column F, it is returning an Error #Value!
For Column E, I would like for the formula to return a value only if the corresponding cell in column G has returned a value, BUT with the next chronological number, and to be blank if there is no value returned in the corresponding cells in column G. So Cell E17 should be Ride 2.

My other issue is that I would like any format of the mandatory dates (cells B11:B13) to be highlighted and my formula only highlights the full format.
Can you please, please help me? And thank you too.

Pl see attached file.

Hi
First thank you so much for your quick response. I changed the formula and it worked fine, and also learned a little bit on the reasoning of the IF function, thanks to your explanation. The significance of column F is that it populates data in columns C & D.
I uploaded the revised sheet. For column E, it is really important that for the numerals 1-9, they show as 01-09. Also, if you look at cell E26 (and following), the return goes back to Ride 1 for some reason.
What I am looking for is for column E to fill only if there are values returned in column G, for the subsequent rows to always add 1 more to the number in the previous cell, and also to show as 01-99 and not 1-99.

Thank you so much. I updated my workbook with the hidden column G. I cannot split columns A-D as the results are used to populate other software.
Appreciate all your help.