Some of the work at home tasks for this career are a bit oddly worded.
For the "Check in at..." try to interview one or more people at that location and/or discuss fashion.
For "Sketch for 2 hours" requires the Digitalistic Sketchpad. Perhaps the bug for this has been recently fixed, but it can be completed if you select "illustrative painting". Haven't tried the other options, but the "sketch impression" doesn't seem to fulfill the task. The inspired moodlet was active which might have helped, but I'm not sure.