Has Anyone Seen Pics Of The J6 Gallows Being Erected Outside The Capitol?....

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7. I'm not finding any images of it being constructed

I did find that, there were actually three nooses among the mob that day:

Snopes:

This was not the only noose on display as pro-Trump extremists stormed the Capitol. Photographer Victor J. Blue captured another that showed a Trump supporter carrying a make-shift mannequin with a noose arounds its neck and the word "traitor" written across its chest.

At least one other noose was displayed during the riot involving a camera cord. At one point, a group of rioters grabbed and destroyed camera equipment...

And, according to this NBC Washington story, the noose from the gallows is in FBI custody:

...No one has been criminally charged in connection with the noose, which is in the possession of the FBI’s Washington Field Office after being found by Dutch journalist Michael Persson, who picked it up as rioters departed...