The only difference between a fixed gear bike and a SS is the rear cog. To covert a FG to a SS, spin off rear cog, spin on freewheel. Your bike shop will do it in time it takes you to decide whether you want to buy 'this helmet' or 'that helmet'. Seriously, it's not even an issue.
What IS an issue, is that you'll need to have front and rear brakes on your SS, which is just a matter of making sure you buy a bike with them in the first place.

And while we're at it, your landlord is a dick. Ignore him and take your bike inside ... and be sure you don't damage the wall paper. This is one of those cases where it's usually better not to ask permission. Sounds like you did and he said 'no'. If you'd said nothing, he probably would never have even considered the question.