the citidel

For the Citadel and the Power Armor, just refer to Imaloony's answer. But I also know another way to get the Gatling Laser. Once you do the quest where the Enclave comes, just explore the Wastes and you will find some Enclave Bases and one of the Enclave Soldiers might have one. You could also find some Brotherhood Outcasts scouting the Wastes and one of them might have a gatling laser and if you follow them, or just check up on them every so often, they might find an enemy and might die from battle so you could take the gatling laser from their dead body.

Citadel: At the end of the quest, "The Waters of Life" you will be granted access to the Citadel.
Power Armor Training: Talk to the leader of the Brotherhood of Steel and ask him for permission to get power armor training (While you're at it, as for permission to trade in the armory). He'll allow you since he knew your father a long time ago. He'll give you the name of a Brotherhood of Steel member who will train you. During the day, I found him near the firing range. Talk to him and ask him for the training and he'll give you the perk to wear the armor.
Gatling Laser: At the end of the Main Quest "The American Dream", as you are leaving Raven Rock you'll get attacked by a group of Enclave soldiers very close to the exit. One will have a Gatling Laser. Kill him for the Laser. There is also a more powerful "Special" Gatling Laser that can be found (This is simply what I've heard, I have not tested this) in the Deathclaw Sanctuary near a dead body at the end of it.

Hope I helped.

Citadel:Either Complete Waters Of Life Quest Or Glitch Inside (See You tube vids For More Info)

Gat Laser: ANYwhere where people carry them (mainly On Enclave Soldiers) Kill Them Loot The Bodies ANd It ShOuLd B In Ur Inventory

Complete the mission "The Waters of Life".