Hi,
No it's not for real it's the internet....
What is real is to go into an island ticket agency and ask them, they know what is going on and you can buy tickets on any of the ferries. I stem from the pre-internet era when that was the only way to get up to date information on ferries, and I still do that.
Kos > Patmos > Samos(Pythagorion), Nissos Kalimnos, to Patmos Dodecanese Seaways, Bluestar.
Patmos > Leros > Kalimnos > Kos > Rhodes, Dodecanese Seaways, Nissos Kalimnos, Bluestar.
None of what you have is at all difficult, quite straightforward.
Should the 'Nissos Kalimnos' not appear then there will probably be something else as small islands must have some sort of service and there are a couple of small islands between Patmos and Samos.
For your islands it's simpler to do them geographically not dodging around, start/finish on Samos/Rhodes.
The 'Nissos Kalimnos' is scheduled from 1 May. Currently in Keratsini, I guess for annual servicing.
You can monitor it here:
http://www.marinetraffic.com/ais/
Schedules for what you require are here:
http://www.gtp.gr/
It's relatively easy going through the Dodecanese islands as they are in a simple straight line, none of the complex crossing ferry routes in the Cyclades.