Has anyone here ever tried playing a psychopath playthrough where you kill everyone and everything? I know that it can be done in F1, F2, F3, and FNV. I'm not sure about Tactics though.

I've seen some videos on Youtube where the player does this kind of playthrough. Obviously, this is a very evil playthrough. In New Vegas, you'd have to side with Yes Man end game. Gamefaqs has a text of an evil karma character that wracks up as much negative reputation as possible wiping out entire towns. Another one for Fallout 2 says that wiping out entire towns is strictly for evil dimwit characters.

oh yea all the time, anyone who plays the games a lot will do various buiids. Fallout 4 is my favorite of the fallout games and i've done a dozen different builds, including just "kill everything" build. I call those my RAIDER builds, where your goal is just to survive and wipe out everything. No vendors, no interaction, no chatting with people. Kill everything, good and bad, until you are the last one alive.

of course some games you actually need to do some things to progress the questline so i don't consider essential conversations/quests as part of the build, but you get the idea. There are dozens of builds to try and a lot of fun in such different tactics.

Fallout 4... minuteman build (laser muskets only), ghoul build (radiation perks), power armor/melee BOS, energy weapons Institute build, Railroad heavy gunner, merchant build (no offensive perks), and many others. Then you get harder builds as you get better at the game to restrict and make it more fun. Charisma only perks build, Stuff like that.

I've read that you shouldn't start killing everything until you get better equipment and have leveled up until you are strong enough to take out anything.

You can't kill the overseer in the first game, turn Arroyo hostile without ending the game in the second game, nor can you kill children or certain essential characters in 3 or New Vegas. You also can't kill Yes Man in New Vegas either.