hi.
I don't see settings in k2 to show lead article, after click on read more user redirected to register/login page.
Or how to list titles article for group registered but show public. 
This is possible in k2?

K2 is using for news portals i don't believe that it cannot be achieved.

I thought k2 had this built in as options, not that you need to additionally write a function that is in the core of joomla articles.

Fotis I always prefer K2 but very long time there was no new feature added.
Com content he just caught up a while ago and many people advise against k2 in favor of com content.
There were turbulences with k2 v3 and many people got discouraged because nothing happened with k2 for a long time. Fears remained about whether he had not been abandoned.
Two years ago, you announced the PRO version and I was the first patron to support you.
So believe me, I am aiming for a big liking for this extension ;)

I find solution module RAXO this is only one module in whole joomla eco system for support this function. But this is always module not native function k2.
Regards.

No other module is just raxo. This is not like a couple of years a go Joomla 1.5 where you could choose between solutions.
I also have no problem to buy a third-party module and pay. ( I have this module and pay for several projects.)

It's more about when the page is standing and you need to rebuild 50 menu items, change the view under the module and stop using the k2 menu category display.

This is a good solution if you create new website. You have to agree with that.

I would like to use an overwriting template, but you propose the solution from the programmer's position. And something that is easy for you because you built the whole component is not easy for another person. (This is the curse of knowledge.)

Even if i want try doc dev is not available getk2.org/documentation/category/documentation/for-developers

It is also not that I require anything from you.
I gave a suggestion whether you will use it someday and you will want to add new options to k2 depends on you, the creator developer cck k2.