ADSL is not considered a "true" modem because it is completely digital and does not perform the modulation and demodulation (mo/dem) of converting analog signals into digital ones.
no
Because you use different modes to access it!
If it's modulates and demodulates a signal then yes, it's a modem.
You might be able to get them off of eBay or Craigslist. You can usually get them from your home phone carrier.