Happy to help out!
I recently purchased a home that has an existing wired alarm. I say wired because I do not see anything that would indicate that wireless sensors exist. I have two DSC PK5508 keypads.
If you have a wired system there will be a control board, typically in the basement, in a metal casing. This is where your sensor and keypad wires travel back to.
Can I simply replace 1 of my keypads with a 2GIG or Qolsys?
You can typically reuse cabling if the run is not too long for the gauge of wire. Wired system keypads will use four conductors, so you can double up on positive and negative to avoid voltage drop.
However, you cannot simply power the new panel off of the old panel board where the keypads are wired to. Always use the included plug in power supply.
What do I do with the other keypad?
The other keypad can be removed and the cabling removed from the old panel board. The keypad will not in any way function with the new system.
Any issues with using wired and wireless sensors with a system like this, (assume not)
If the system only has two wired zones, those can be wired directly into a 2GIG Panel. (There are two hardwired zone inputs on the terminal block)
However this would require getting cabling up to the panel location from the sensor wires. What is typically easier is to use either a 2GIG Takeover Module, which converts wired zones into wireless ones, or if you only have two wired zones, it would be cheaper to simply use two DW10-345 sensors. The DW10-345 has a wired input which lets it act as a wireless transmitter for wired zones. See this programming guide post for more info.
Similar options are available for Qolsys.