I changed ISP, so I changed IP at my registrar's DNS settings to point again to my unchanged NAS, while adding a new router for 1Gb network.
Then after 24hr my non-WP sites were fine but the WP sites were not loading, took like 1 minute. I deactivated all plugins by renaming the plugin-directory, then the WP sites were loading faster again. Then logged to the admin dashboard (still slow too however), and set back and activated the plugins again. Now it all works better, also the admin dashboard remarkably now works better again.
It's a little bit back to normal now, but I still see few seconds delay when browsing though my sites, it feels a bit like it has to 'wake up' somehow. It takes still few seconds for the first things to appear, sometimes even 30-40 seconds or more when you wait a minute before clicking the next link.
I'm not sure if this is really related to the ARP/network mentioned somewhere else. I'm still puzzled about this, particularly as I hadn't changed anything on my NAS(webserver), and it's using the same IP towards the new router. The old router gave the same slow results by the way (replacing new router back with old), so I suppose it's either the changed LAN connection (indeed ARP?), or the ISP (but seems odd) , or it's the fact that the NAS does not properly see the domain name itself when it's creating the pages...