When will the latest beta version become official and how stable is the beta version and are there any bugs in it? Thank you and have a nice day!
The developers are pro bono and work on K-meleon in their spare time. As both of the main developers are Europeans right now, that means June for the next official update.
As for current releases. K-meleon 1.6, beta2 is pretty good. I am using it in place of K-Meleon 1.5.4, which was the last official release. I moved to KM 1.6 because it uses the newer Gecko 1.9 engine (KM 1.5.4 uses Gecko 1.8). If you do go for the KM 1.6b2, ask here for help with fixes that have not shown up on the wiki Download.
And yes, there are always bugs, but none to my mind that are critical. Others may jump in here who have beeter technical knowledge than I do.