Electronic speedometers/odometers do work in both directions. The old cable driven speedometers/odometers ran backwards in while reverse.
Speedotomoter Drive Gear
It'd be rare for a bike to be sold with one, but it's real easy to buy and install a bicycle computer, which will have those functions and more.
Yes. Polar has one for instance. Probably Suunto and Garmin has too. They're more than odometers though, so be prepared to pay nicely for them.
1
Yes
Km/h
An odometer is a machine that displays distance travelled. Odometers can show any number of digits ans so any number of miles.
A bike in good condition will work at anytime and anywhere.
The gears inside the odometer broke due to heat and age. You can buy the gears and replace them yourself. Or you can take your car to a place were they work on odometers.
If the bike came out with blinkers , they have be on the bike and work .
If you like to use an exercise bike to work out, and don't mind some noise and wind, the Airdyne will give you a great workout. You can buy a good bike at amazon.com