It works with a broadband connection. dsl=broadband, therefore should work (unless you have a slow dsl connection.
Most POS machines these days can still use phone connections but also accept DSL.
Serial
Yes a DSL, or Digital Subscriber Line, can definitely be run into a personal residence. A DSL connection can be easily achieved with either wired or wireless broadband routers.
dedicated shared
No, DSL modems are meant to receive data directly and are unable to dial. You will need a modem with dialing capabilities to use dial up.
Dial up internet connection? Yes it can but it is recommended to use DSL or any high speed internet connection since VoIP rely on internet.
In order to have a phone line connection that is as fast as a Local Area Network connection, or almost as fast, you'd have to be connected via DSL. Verizon offers a really neat DSL; this is what I use to connect. DSL's connect through the Ethernet port on the back of the PC.
Open voice dialer app
DSL is sually faster because you are not sharing the line. Cable slows down as more people use it.
You can have a DSL line without a telephone number. You can then use an inexpensive voice over IP service like Skype.
When you say "connect it to the wall jack", you have DSL connection or cable connection? Does cable connection allow the use use of a wireless router and card