If the alt account itself was not made until after the last mirror (which was on February 15), then the alt account won’t be able to log in to Singularity at all.
If the alt account was made more than a few days before the mirror (because it isn’t clear the exact date of the image used to create the mirror, only the date the process was completed), it should be able to log in - unless you changed your password after the mirror.
With regards to the transferred character: just like with a password change or account creation, if the transfer was done after the mirror image was taken, then the account transfer of the character hasn’t occurred in Singularity.
All changes made on TQ after a mirror won’t show up on Sisi. CCP has added a tool to allow players to import trained skill levels (from a nightly completed skill image they take out of TQ), but that’s the only post-mirror activity that can be refreshed - and it has to be manually triggered using /copyskills on the desired character.