For the same price or less I'm sure we could help. Our shared plans would be able to handle that many products and images without issue. See our magento optimized shared hosting for details. Our support will help you configure Magento for performance.

I should have probably added that when possible it's always preferred to use cron.sh over cron.php to avoid the multiple instances running like Melvyn mentioned.

Ok here's a quick breakdown for things to look at: 1) Setup full page cache (google this for Magento) 2) Evaluate pages that have too many items loaded and setup a lazyload extension 3) Need to optimize Magento database (hopefully your host has expertise here) 4) Get web server with fast CPU (GHz). This will directly impact the speed at which the PHP files can be processed and loaded. SSD on the DB server will help too. That's a very basic outline. Above and beyond that it can be very complex. Find me on linkedin and I'd be glad to look at it with you and lend a hand.

Check your app/etc/local.xml file. There should be a part that indicates where your session files should be stored whether that be files, database, memcache, etc. If not already set to files try changing it to files. Easier to debug. The code looks like this: <session_save><![CDATA[files]]></session_save>

Your site should definitely have an app/code/core/ folder. That is where all the "core" parts of Magento are found. If you have things in app/code/local/ or app/code/community/ those typically just override what is found in the app/code/core/. Is the site currently working despite the error message? If you do not have the core directory you might try download the same version of Magento and copying that directory into your installation. Is there a link you can share for the site?