Looking at the product page of your website, it looks like the
2GIG-SMKT8-345 is the proper replacement. Is this correct?
Yes, the SMKT8 is the replacement.
My alarm panel continues to produce an audible alert telling me about this fault. How do I deactivate this alert until I can install the new alarm?
You can remove the sensor from programming by following the instructions here.
In your post you referenced the manual. I do not have one, so how can I get one?
You can download the manual for the SMKT3 here.