The slash command is /architect, however, you need the Mission Engineer badge to use it outside of an AE building.
https://homecoming.wiki/wiki/Mission_Engineer_Badge
"Invisible" wasn't mentioned in the original post or any subsequent post. The post asked for Stealth, "real stealth" and the responses were based on that. Perhaps the intent of the question did not take in to account the nuance of how Perception and Stealth mechanics work in this game, so the right question was not asked.
For example, the power "Shinobi" from Blaster Ninja Training grants +35.5 feet StealthRadius PVE (self only) - same goes for "Field Operative" from Blaster Devices which grants +35.5 feet StealthRadius PVE (self only).
The "Celerity: Stealth" IO slotted in the Sprint power grants Blasters +30 feet StealthRadius PVE (self only). Use Shinobi + Sprint slotted with Celerity: Stealth to get +65.5 feet of stealth.
As a comparison, the power "Stealth" from the Concealment Pool grants Blasters +55 feet StealthRadius PVE (self only).
Blasters are not getting any higher stealth from any other powers outside of temporary base empowerment craftables by themselves. Ask someone on the team for "Grant Invisibility" and you'll also get another +55 feet StealthRadius PVE (self only).
Then take in to account the amount of Perception that certain mobs have in-game. Some will see through any amount of stealth.
I have soloed all content in this game outside of the things teammates are required to start (incarnate trials, MSR, Hami, etc.) with my Ice Blast/Cold Domination/Ice Mastery Corruptor. I have every souvenir, collected nearly ever badge (outside incarnate content and Master of stuff), and played the same character for over five years now. This anecdotal evidence implies any other Archetype and powerset combination could also do so under the same constraints.
It sounds like you're really digging in to the way powers works to get the most out of your build - I would recommend visiting this site to get the details that aren't always reflected from the in-game power info:
https://cod.uberguy.net/
It's not too late. You can unlock a contact (on both Hero and Villain side) that allows you to pick any Safeguard or Mayhem mission without doing the 5 prerequisite missions. You just select which one you want then you run it.
To your second question, yes they count (there is a certain distant that it stops counting though - dunno the distance).
Badge defeat guide says: Typically the best way to fight these is during Mayhem missions. They do appear in some high end redside missions, but some may prefer doing mid level mayhem missions (Brickstown /IP/Talos) for Paragon Police as they are a rather difficult enemy group at higher levels.