Leather restaurant check holder

Hi all, I am getting started on a beginner project for a friend - making a simple veg tan leather folder for his restaurant staff to deliver checks to clients. Objective is to have an eventual saddle tan color that shows patina with time and I will stamp his logo on the front. I bought natural veg tan have a few questions and would appreciate any guidance. Here are the steps I have taken thus far:

A) I cut the leather 8.5 wide by 9 inches tall; 3.29mm thick

B) I placed them outside to tan (only one day so far but will want a deeper color).

C) I made a simple, flat wooden "mold" by cutting a piece of 6mm wood (see photos)

Questions for community:

1) Should I coat them with linseed oil prior to tanning to prevent drying? I don't want them to be super stiff and will want to prevent drying out over time.

2) How do I work to finish the raw, flat inside to make it a bit smoother? Should I skive it down/split it to be thinner?

3) How do I make a cut in the center to allow for an easier fold? I tried using my edger but it is not getting the deeper, wider groove desired.

4) I tested soaking a piece of leather for 15 minutes in water, then molding it (without the groove). It is a bit thick and doesn't close flush, so the groove I think is needed. But once dried, it is super stiff leather compared to the other pieces not soaked. Any mold advice?

Thank you all for any contributions on my "hands on" second project after simple belts!

Best,

Elizabeth