Very poor print quality

did you stop it half test and see where the quality issue is... tech 101

You have purchased a bad drum. Replace it again.

I'm more familiar with HP printers, but it sounds like a fuser is bad. The fuser effects print quality as well. If you've replaced the toner, as you have.

I would say you have a bad drum / toner cartridge.

Stuff you receive with vertical lines is probably the sender's dirty scanner.

My good friend:

The only reason why your unit stops printin faxes is because the toner cartridge is nearly empty. Th e unit will then try to conserve the remaining toner for printing and copying. Follow this steps to program the unit to print all faxes, even with toner low:

When the toner cartridge is nearly empty, the machine shows
the “[Toner Empty]” message and continues printing except
incoming faxes. In this case, incoming faxes are saved in
memory.
However, you can set the machine to print incoming faxes, even
though print quality is not optimal.
1 Press Menu until “Machine Setup” appears on the display.
2 Press the scroll button ( or ) until “Ignore Toner”
appears on the bottom line and press Enter.
3 Press the Scroll button ( or ) to select “On” or “Off”.
Select “On” to ignore the [Toner Empty] message.
Select “Off” to stop printing incoming faxes when the
message appears. This is the default setting.
4 Press Enter to save the selection.
5 To return to Standby mode, press Stop/Clear.

Be blessed

Probably caused by the toner cart. Only use genuine new Brother brand supplies. Remans fail quite often with Brother machines.
Possibly bad gears on fuser drive. But with the poor print quality, I suspect it is the toner.

beware of generic toner!
you may need to change out your drum unit
the drum unit may have been contaminated by the staples toner.
also clean laser window under drum cartridge.

turn off overseas mode

can only be toner, drum or fuser, pull out drum and look at surface are you streaks present? usually drum.

Stop a print half way threw machine and then remove drum and look at print, pre hot bit (fuser) are you marks there? If so it is drum, if not fuser.

Are you using genuine Brother supplies? Generic supplies are the main reason for print quality issues. Have you ever changed thr drum unit ? Expensive! You can buy a new machine and get a new drum and toner for a little bit more.