A RO membrane works better if you make your water in larger batches. Short filter runs lead to TDS creep which shortens the DI life.
I leave my RO/DI hooked up all the time but I have float switches filling an ATO reservoir. The system you are looking at, which I highly recommend by the way, is set up to make water manually so you can either disconnect it after use and store it with the housings full of water in a closet or other out of the way places until next use, or you can buy a 1/4" John Guest style ball valve from the local hardware store and install it on the inlet of the RO/DI, shut it off and leave it connected. I prefer to leave things connected as it is less prone to leaks and drips that way. It can stay unused for 10-14 days no problem as long as it is in a climate controlled place and out of direct lighting.
You can store RO/DI water almost indefinitely as long as it is sealed or covered with a snug fitting lid in a bucket.
Yes, a handheld TDS meter is the best way you have of determining how well the system is working and when you need to replace the RO membrane or DI resin. Stick with something like the HM Digital TDS-3, TDS-4TM or AP-1 as they are all ATC temperature compensated unlike the TDS-EZ or inline meters.