Unifi. Just works, does everything you need. Simple UI, lots of different hardware.

No. A PoE injector will simply ignore any PoE coming in on the data port. Why not use a PoE powered switch like the Unifi Flex? I used several of these to power multiple cameras where I only ran one PoE cable to.

100% agreed, yet, pointing out all options available is a nice thing to do.

Do you need a cable or is a good Wi-Fi connection enough? You have three options, since 26m is not very far.

1. Run fiber. You can use so called media converted to convert from ethernet (copper) to fiber, you need them on both ends, they both need power.
2. Run an ethernet cable. Since it runs outside, make sure you use a S/FTP cable that is properly grounded on both ends and use ethernet surge protectors to prevent your gear from being fried by lightning.
3. Install a directional Wi-Fi access point on the outside of your house pointing in the direction of your garden office.

No. In all cases all devices have maximum speed of your network equipment and themselves. I think what you meant to ask if a switch would reduce the bandwidth available to the devices, which is also a no. Both PC’s using the internet at the same time will reduce the bandwidth, but not 50:50. A normal unconfigured router will give 100% of the bandwidth to each connection, meaning, if PC A is downloading a 1GB file that takes 10’ to download, the internet for all other devices for the next 10’ would appear to be very slow, till that download is finished. A more advanced router, would reduce the bandwidth of PC A to like 70% so that 30% can be used by PC B. In any case, the network equipment you use, as long as it is faster or the same speed as your internet connection, and not connected by dozens of switches, will not slow down your internet. Multiple clients do. I have a network of over 250 clients at home, so there are rules in place to guarantee the bandwidth needed for certain devices (like TV’s for streaming) where as other devices (like phones or tablets) are less prioritized.

You put switch thingy in there, connect all ports to switch thingy. You connect modem LAN port to any room port (so it connects to switch thingy), and connect modem to WAN via VDSL in room where VDSL available. Dumbed down enough for you?

Alter, kauf dir ein Switch, steck alles dort ein, pack dein Modem dort hin wo du das Internet bekommst (VDSL: Telefonsteckdose, Kabel: Coax), verbinde den LAN port von deinem Modem und voilà jeder Raum hat Internet.

Over what distance? What bandwidth?