@An Enemy Spy: Advanced Infantry Equipment is too broad. Armor for your units will require some kind of Armor tech (Basic Infantry Armor is the most obvious of these, though you can be creative here), and infantry weaponry needs to be specified (Basic Infantry Lasers? Railguns? You've got options).
Advanced Propulsion works. Unless you're looking for a new propulsion tech, this'll translate as Improved Nuclear Drive. Note that having an upgraded tech doesn't give you the upgraded facility/module by default, you have to spend one of your freebies on that (the one that gives you two facility/module upgrades).
Propaganda Machine works just fine. This will be called Basic Propaganda for the base version. Fancy tech names work better for upgrades.
As a note, depending on what kind of Government tech you end up picking up down the line, it might give bonuses to this.
A Fighter is actually a culmination of several techs. You need some sort of vehicle weaponry (Basic Vehicle Lasers or something) at the very least, and I'd recommend having some kind of hangar too. Launching them from your cargo bay will take a very long time. All space vehicles require some kind of armor, though Hull Plating works in a pinch. Armor would be better for them though (or Shields), and researching Basic Armor applies to both vehicles and ships (you don't need a separate tech for defensive options between ships and vehicles).
Basic Espionage and Military Chain of Command are both fine, as mentioned in earlier posts.