Go to the Armory. You will see you sniper rifles, assault rifles, etc. In the bottom-right, select ADVANCED WEAPONS. This is where you can choose, buy, or make the special weapons. BUT...you can only use them during the special events. You can't use them at all in the normal events. Does this help?
I don't know which one is specifically drone 34, but for the headshot levels, often it's ALL of the Objectives that need head shots and not just the primary one. (It doesn't seem to matter for the low-priority ones). Does that help?
Could you clarify this? If you want an advanced weapon, often you need a design then fabrication. But the latter requires you to collect "parts", like triggers and things. For that, you need the Alerts and daily action. Does that help?