I am not able to install available apps on my watch. My watch and iPhone are fully charged and on the same WiFi; why can’t i install an app on the list?

If you followed the steps in the 'Install apps you already have on iPhone' section of:

Get more apps on Apple Watch - Apple Support

then the first (and simplest) thing to try if something isn’t working right is to restart your Apple Watch and its paired iPhone. If necessary (device not responding), try a forced restart. Both methods can be found here:

How to restart your Apple Watch - Apple Support

Restart your iPhone - Apple Support

If that doesn't help, the next steps would be to unpair and pair your watch again and restore from the backup just created. This should result in no loss of data. It deletes all temp and corrupted files and re-indexes the file system.

Unpair and erase your Apple Watch - Apple Support

Set up your Apple Watch - Apple Support

I am not able to install the app from play store after putting user name and pass word.

it shows the operation coulnot be completed(com.apple.commerce.client.error500)

Do you mean the App Store?