Ok, so before we get into the questions themselves ... lets first talk about the series of tubes that is the internet.
In pretty much ALL situations you have a device (home computer) that connects to a router (home router) that connects to your ISP's router which connects to another internet router that may or may not be within the control of your ISP.
So ... in other words its routers all the way down.
This means that your non-encrypted traffic is not really in any more danger from your neighbors than whoever your ISP connects through to get you to whatever site hosts the HTTP site.
The issues posed by your Landlord's setup are as follows:
When you plug your computer into a home router you normally get an address like 192.168.0.x. This is known as an "internal" address and normally makes use of your home router to bridge traffic between Internal and External internet. The problem with your Landlords setup is that all 4x neighbors will all be on the same internal network ... eg you could theoretically print stuff on one of your neighbors printers or ddos their Ring device and lock them out of their house. The solution to this is either the Landlord setups different VLANs for each of the neighbors or you do it yourself by connecting a home router to the shared router (thus creating your own private network inside their network).
If one of the neighbors does something illegal on the internet connection it will be very hard to determine who done it. Unless the Landlord logs the traffic as well as ISPs are generally required to do (highly doubt the Landlord will do this ... and thus is prob the one taking the risk).
If one of your neighbors decides to consume all the bandwidth it could prevent anyone else from using it till they are done and/or get the shared connection throttled.
If one of your neighbors does something bad (though not necessarily
illegal) they might get your shared external IP banned from services you frequent.
with 4 flats using it the password will be common knowledge
I don't see this as being a huge problem ... All the people at a Starbucks or McDonalds know the password and share. Its less about the password and more about the interaction between the devices on the network itself. Most places that do public shared internet setup firewall rules such that communication can only occure between devices and the internet ... not other devices on the same network. Though, your landlord may or may not know how to accomplish this as it can be a bit technical.
whilst I can use a VPN for my phone/pc I can't for my printer, so
either no network printing or anyone can access it
This is a non-issue if you connect a home router to the shared network, and setup a VPN on the home router. All devices on the inside of your network will make use of the VPN. Though this doesn't really buy you much as all encrypted traffic is encrypted already and all non-encrypted traffic is still not encrypted when it exits the vpn. VPNs are kind of a sham unless you really know what your doing. This should cover ALL your questions regarding VPN.
Alexa / network storage / plex server ... will this be insecure/even possible?
If your landlord doesn't setup VLANs for each of you and you dont use your own home router ... yes, you will have problems. Though these are all solvable problems as described above.
