If a group of minions do not have the skill listed, do you upgrade the dice like normal?

For example, a Stormtrooper has Athletics and a Brawn of 3. A single Stormtrooper would roll 3 Ability dice. A group of three Stormtroopers would roll 1 Ability die and 2 Skill dice following the rule that minions gain 1 rank per each minion after the first.

So if a Stormtrooper does not have Vigilance or Cool on his list and a group of three Stormtroopers needs to roll initiative, do they follow the same rule? If not, would they just roll their ability dice without ranks. For example, do they make a single Cool roll with 1 Ability die for his Presence or a single Vigilance roll with 3 Ability dice for Willpower.

No they do not upgrade unlisted skills. So all ability dice for cool and vigilance

Ultimately, its up to you.
I personally don't modify anything unless they have some kind of equipment that gives them an advantage. The point of minions is that there are A LOT of them, so they don't need to go before the Pcs to do damage. They'll probably survive the first volley your players throw at them.