- it is a second-level domain, why?

- 9 characters (home.arpa) is a lot

I kind of understand the motivation, it is a "technical" domain since it doesn't represent something in the global DNS registry, so it gets the .arpa TLD. However, that's reasoning that it out of touch from normal users. Normal users don't want to be exposed to the technicalities of DNS when they enter something in the address bar, and "myserver.lan" is more meaningful than "myserver.home.arpa", and giving meaningful names is the whole point of DNS.

I can't fucking _wait_ to type bender.home.arpa instead of bender.lan. Hyped.

Search domain is handy but it's ambiguous.

I don't know what this means, and searching is thorny. Help?

Your DHCP/SLAAC RA tells clients "here is a list of search domains, when you attempt to query a bare name, also look for the name plus any suffixes listed in the search domain list". So on a system with "home.arpa" in the search domains, you can do something like 'ping myhost' and your system should attempt to resolve 'myhost.home.arpa'.