I do not recommend providing a live copy of your site. I cannot guarantee the review won't break something.

You should provide a clone of your site instead in a subdomain or subfolder. The best way to do this is to typically make a copy of the database, make a copy of the site folders structure into your subdomain or subfolder, adjust configuration.php to point to your copy of the database, then turn off emails globally in Joomla (so the test site doesn't email your users). Things can then be safely debugged without impacting your actual site.

The PHP temporary directory is the one that PHP uses to store a saved file before Joomla can access it. While the lack of definition is not always a problem, if you have errors regarding not detecting sent files or manifests, setting this directory in your php.ini file might fix this problem.

Yes, that absolutely will cause problems. Files are uploaded to PHP tmp before moved to Joomla tmp for install. If there's a permissions problem with PHP tmp or Joomla tmp then things will either not install or only partially install.

Contact your host for server related configuration problems. PHP is not setup correctly if it's tmp directory is not accessible or doesn't exist. This is specifically referring to upload_tmp_dir in php.ini.