Weird Errors: do_action('wp_loaded')

Hi guys, two things have started happening in the past week to my wordpress site.

Firstly the error which is in the title .0 */ do_action('wp_loaded'); ?> this seems to be causing problems in the back end of the site. If I make a post for instance and then hit ‘Publish’ it just brings up a blank page apart from that bit of code at the top. The post still happens but it just doesn’t return you back where you should be.

This error is also running throughout the site on the front end and within certain boxes on your dashboard.

The second error and also the first one I found was an error about “Allowed memory size XXX exhausted..”

All these things have happened over a two day period and now im worried im going to lose stuff, or brake something. Can anyone help and also recommend a safe way of backing up all of my data. I need to upgrade to the latest wordpress but my server doesnt have the latest version of PHP yet, so the host said I need to back up and then move over to a new server.

Thanks in advance for any advice
Cheers
Steve