User Manual Cuisinart CPT-T40 4-slice Touchscreen Toaster

The product page has multiple items for sale by the same manufacturer, so all the reviews are lumped together.

No - not at all. It recommends not to have it under a counter
during the brew cycle, so I pull it out from under my cabinet until
after brewing. There's a small vent on top.
You an leave it on warm plate for quite awhile but if you are
finished for the day, clean it up and wipe it down or unplug. If
you unplug you have to reset time.
I am very satisfied with this coffee maker.

I believe because it has a feature to pause the flow of coffee when
caraffe is removed, it will not dispense coffee without the caraffe
inserted.

No, according to the manual you can adjust the temperature but
NOT turn it on by itself. If you want the coffee to stay hotter longer
look for a coffee maker with an insulated or "thermal carafe". Or
replace the glass carafe with an insulated thermal version.

Yes, but programming auto brew or auto shut off isn't difficult, but it
isn't easy - it is tedious and cumbersome. Why not just make a icon
for brew or shut off that you tap once?