Important Installation Error

Good! Before you contact your hosting provider, try again but this time start with Kunena first and make sure that you can do that much at least. Add other components, one at a time, and test that Kunena still works. It's a mongrel of a job, it's time-consuming, but eventually it will pay dividends for you. The best part is that you have a test site for future use!

It seems that Joomla installer fails for some reason.

This error has nothing to do with Kunena itself. As sozzled suggested, there can be few reasons why installation fails for this component but not for others in a clean site:

Try to install another package (gzip/bzip2 instead of zip): package can be corrupted or your zlib version is buggy.

If it does not work, look into the temp directory that the file actually exists and that permissions in the destination are ok.

If you have still some issues you can make a new package by extracting and compressing the file again.