Both options are available, so ask your agent about both before deciding which one is better for you.
Yes, the wireless system will connect through home's WIFI connection.
There are many different options available, but most homes are secured against home invasion as well as smoke and fire.
No, but that feature is available. If you are interested, inquire with your agent and they can provide details on options and costs.
This will largely depend on the type of system you have. Be sure to inquire about the reliability of the system during a blackout before making your selection.