What are some options to reduce smoking out an apartment while cooking?

I don’t have any suggestions, apart from

a) opening the windows or
b) paying more attention to your cooking.

Do you use a high amount of fat when frying?

My smoke detector has a button that stops the ringing. Sort of like sleep mode. Check your smoke detector for a button that switches off the buzzing.

do not turn the stove to full whack.

I would concur with @ragingloli. If your frying oil is smoking, your fire or burner is too hot.

Switch to steaming or pan-broiling?

I can feel for your situation. I was living in a small apartment not so long ago. The stove had an exhaust fan, which went right into the cabinet above!
Use a crock pot when you can.
I reduced frying time on some foods by boiling, baking, or microwaving the food to almost done, then only finishing in the skillet for texture and flavor. I switched to (ugh) microwave bacon while I lived there.
The best you can do is alter your cooking style a bit, unless you can convince your building owner to make some new ventilation in the units.

Use an oil that has a high smoke point.
See the attached chart of oils and their smoke points.

Use safflower oil it handles the higher heats with less smoke, corn oil is a good second choice and avoid vegetable/olive oils as smoke a lot more at lower temps.

Also, hemp oil, if you can get it in food grade, has a high smoke temperature

I’m with those who suggest not having the oil too hot, @LuckyGuy suggestion about trying an oil with a higher smoke point sounds like an excellent idea.

Are you pan frying, or deep fat frying. If it’s deep frying, you can buy appliances that are completely enclosed when frying, that have a filter in the lid, like this one.

Even better, if you have the bucks.

Check this out!

There are all sorts of hazards involved with letting your cooking oil get this hot. (I agree with others here that it is too hot.) They have linked a higher lung cancer risk because the oil becomes aerosol and is breathed in and cheap oils contain carcinogens. See attached study: http://www.phys.hawaii.edu/~sattler/Publications/pdf-files/Aerosol%20of%20Hot%20Cooking.pdf

Lower the temp and get better oil.