I am new to Foundry myself, but I have learned a little bit.
1. How do you get rid of the spinning "War Paused" logo?
2. Does Foundry track ammo expenditures during combat? If so how do I work that?
The weapon has a magazine in it, if not, you have to put one in. If you edit the weapon on the character, you can both generate ammo for it that will appear on the character sheet and you can also select which one of those magazines to be in the weapon. If you attack with the weapon, it will deduct ammo automatically. At least if the character is a PC, I am not sure how it works for NPC to be honest (I have to do a test fight to check that out).
3. If a character attacks with a grenade or other explosives how do you bring up the radius and apply the damage?
In my test fights I have not used grenades yet, so I will have to come back to you or perhaps someone else will answer this that actually has some experience with this.