Found a nice guide showing cable length recommendations per wire gauge and impedance putting the max length at 48 feet for your specific situation: https://avgadgets.com/speaker-wire-cable-gauge/ I would recommend a dedicated amp just for the media room or living room depending on your needs, especially if you’re considering a 7.1 setup (Dolby Atmos is the current must have). As far as the rest of the house, multi-zone amps are not cheap and lack tuners. If you decide on 2 amps, you can locate the multi-zone amp near the media room and “share” different components (like a cable box or media player) to keep costs down.
One last thing, when sitting on the patio, even with the living room speakers just 20’ from the patio door, there is a very noticeable delay vs. the patio speakers. So, although it’s nice to have the ability to play music simultaneously in every room, if you’re between rooms, the delay will noticeable. Good luck!