If multiple extensions are failing then there's certainly a problem on your site. Either with your Joomla install or with your server having bad Joomla permissions.
I suggest posting your issue to the Joomla forums or reviewing Joomlas documentation below regarding this. Please note Joomla nor us can really help you much with this as it's really a host problem.
docs.joomla.org/Why_can't_you_install_any_extensions%3F
In short it's usually due to a bad hosting configuration. Especially if you used your hosts panel to install Joomla instead of unpacking and going through Joomla installation normally.