Thanks Sebastian. There is no proxy between the server and the Internet. Cache settings were default when the problems occurred. I played around with different settings for Page State Persistence, Module Cache provider, and Cache Setting without any luck. Even setting Cache Setting to None the problem still randomly appeared. 

From your hints, I decided to do 2 things at the same time:
- Updated MS SQL Sever 2005 to SP3
- Set page file size to 12288GB (1.5*8GB system memory). The previous setting was 2GB to 4GB if I remember correctly.

Rebooted the server and both the problems magically are gone without needing to change anything else!! I don't know which of the 2 changes above or both have helped to solve the problems because I did both before rebooting the server.

This is quite strange to me but I don't complain because my site is smooth as silk now.

I will report back if the problems somehow come back.

Thanks for all the help guys.

 
That's it! Web Garden was set to 2 and the site still was acting strangely. No refresh problem but still had problem with caching sometimes after making changes to System page file and updating SQL server 2005 to SP3. However, after changing this Web Garden value from 2 to 1 as suggested, my site seems to work normally now.

Thank you thank you so much Sebastian!