I use Directory Opus 10.
I can select Files Count in column chooser while viewing folder content.
Is there any way, I can view the number of files inside zip file for each zip file.
Also, how do I use preview window to show common image, text files etc.
File Count and Total File Count both work on Zip files, at least in Opus 12.
It's possible it's something added after Opus 10 -- 5 years is a long time -- but I don't have an old version handy to check on.
Try using the Total version of the column in case all the files are below the top level of the archive, since the other one only counts what is directly below and would show 0 files for that.
Turn on the viewer using the button for it in the toolbar (or a hotkey), then select a file.