I'm very new to gardening and this is my first year planting flowers, so excuse my cluelessness. I bought one hanging fuchsia and one hanging petunia (there was no petunia section, if anyone can offer feedback about them too I'd be very grateful!). I'm in NYC (zone 7A I think) and have an east facing balcony where they will be staying.

Our spring has gotten a slow start, and we've had consistently cloudy, rainy,
cold weather. Morning temperatures are in the mid to high 40 degrees,
day time temps are lucky to top out at 60 degrees, but have often been
in the 50's.

I purchased them at a Home Depot that was keeping them outdoors 5 days ago. I have watered them twice since then but have yet to fertilize them or take any measures against pests. I have been bringing them inside at night and not letting them out at
all during the days where the temperatures won't stay at or above 55
degrees during the work portion of the day when I'm not home. Out of 5
days they have only been outdoors for 2 of them, and we're set to have
three consecutive days of rain with temperatures between 48-65 degrees.
When they are inside, they do sit by an East facing window with the
shades open, for whatever good that does them with all the clouds.

My question is, what on earth can I do to take care of them during this cold snap? My petunia is resilient apparently, but my poor fuchsia is dropping about 5-8 flowers a day :(

I have a space heater, should I sleep with it on close to the plants
at night haha? I laugh but..I really have no idea. I'm very new to
gardening. Should I fertilize them in the meantime? Any and all
suggestions would be much appreciated, as well as any favorite links to general care for the these lovely beauties. Thanks in advance!