Correct, they also make hybrid photoelectric/ionizing detectors for the best of both worlds. Portable CO detectors are cheap and nice too.
Generally speaking photoelectric detectors can go into the garbage after 10 years, ionization should be taken to somewhere that recycles radioactive materials (Americium-241), which IME is not too hard to find for detectors.
As already noted, yes. On my units specifically, there is a different sound pattern for smoke versus CO detection, and a different LED that flashes in sync with the sound pattern. If and when the source of the alarm is cleared, the light remains on in the unit that triggered the alarm. In my house, if the alarm was triggered by cooking activities in the kitchen, the LED indicator has to be reset by poking the “Reset/Test” button with the tip of an umbrella. 
(Warning, loud)
Temporal 3
versus CO detection
Those are standard sounds and some* smoke (and CO?) detectors actively listen for them and even if they’re not interconnected, will still go off if they hear it.
*But apparently not mine, they didn’t react to me playing samples of it just now.
The manual for my alarm system says continuous beeping is a smoke alarm. Four beeps and pause is a CO alarm. Different LEDs light up on the originating detector depending on the cause.
I have tested mine and besides the beeps, which I suspect are universal, it will say something like “smoke detected - alarm will sound in 30 seconds” so you have time to shut it off if you are blackening salmon in the kitchen or something,
That’s why I won’t move to a house with 9’ or 10’ foot ceilings; no umbrella necessary for me in a standard 8’ house.
I clicked on your link & it took me to a Tempurpedic mattress page; didn’t realize it was an ad at first; especially because the first couple of letters are the same; thought it was a bad link. 
I shouldn’t think the height of the ceiling would be an obstacle for you at all
It took until around 15 years ago for someone to get the bright idea to make the buttons large instead of those tiny little flimsy dots.