You would do almost daily water changes when they are babies due to their sensitive nature. As they get bigger and the size of a plate you don't have to do it every day. Just the first 9 months of their lives are usually the most time consuming hectic time.
The last time I cycled a tank was a few years ago with my 55g. I initially took some media out of my 90 to jump start it but I forgot to add dechlorinator into the tank which killed off whatever I had added from the 90. So I just let it sit for a month, added some food and it was ready in a...
It's likely they're not used to their new surroundings. It's common with fish and it may take time for them to get used to it. I believe discus require more than just the two fish. You will need to add more in the future.
If it were me I would treat this situation as a vacation mode. Don't feed the fish. Do a feeding and a large water change before your surgery, like 2 days before and go on vacation mode. It will be tough since your not on vacation but it will make it easier on your parents, less pressure too.
Since this is a framed tank, as long as all four corners are touching you should be fine. It looks like you added shim's in the middle, which is fine.
If there was a gap in one of the three corners that would more of a concern.