Hello
What can be a reason for points being not visible (with edges and polygons everything is ok) ?
points count, geometry spreadsheet and manipulations show they are selected and when Display Points turned on
thanks

Try selecting the node in the Geometry network that you want to select points on.
Move your mouse into the 3D viewport and press the S-KEY. Choose points as your context drag or click to select.

It's hard to say from such a simply post image, but you may have have visualized something but not selected it..?

Other than that, try the obvious corporate suggestions. Buy a new computer. Update your graphics card to meet the minimum hardware requirements, and or download the latest version of Houdini.

Thank you for the answer
yes to try obvious suggestions was my first idea either
well that's weird - if display / render flag set on node and this node is selected in network - points visusally not selected in viewport; if in network selected another node rather than with blue flag - all points and points selection are visible
variant of course to just turn on Display Points... already not sure maybe it's supposed to be so