Sadly, I don't know any way to connect to a Fritzbox without the client software. What I can find in Internet that a few people have been successful connection to Fritzbox without using the client. The other possibility is with Shrew Soft VPN Connect.
If I have understood your situation correctly, I don't see any possible solution that can satisfy all your requirements. As for the strongswan there is no way to escape using certificates. Because the connecting user authenticates using Username/Password using MSCHAPv2, but the gateway needs to be authenticated in advance using Certificates.
For assigning static IP to the clients you may use ipsec pool tool:
I guess you need to come to a compromise for a possible solution. If you don't want to get into vpn stuffs, you can also think of creating a NAS server and sharing it securely for the user or may be this is also interesting: