1. how do I mention alternate zip method? When I start the backup it doesn't ask me what zip method to use. I used this plugin for several sites ... but it started to give me this error only for the last 2 sites.
2. I did re-save the permalinks each time. For the last 2 sites, the problem was that even after re-saving the permalinks, the other pages were not loaded (the error was something like the page does not exist on the server, contact the webmaster). I was using on my server the permalinks "%postname%" and after google-ing somebody suggested to set the permalinks to "/index.php/%postname%" (which by the way is not mentioned in the suggested permalinks by WP)
So, finally I solved the issue, but just after searching on Google ... WP permalik suggestions and WP Clone did not helped me.
This is what I wanted to highlight, maybe you can find the glitch and correct it (if necessary).
In a couple of days I will have to move another cloned WP site from me to my client and I will let you know if I have the same problem (if you will not find the cause by then).