'moodledata directory there are several folders named '0d' ... well, yes, that possible with hashing, but they do NOT, cannot exist at the same level ... ie, just below moodledata.
The first error you got pointed to a file we created and placed manually.
This next error is for a file that should be in moodledata/a9/6d/
and it's hashed name is a96d80ff2a77aa3fe204e8ce2c4c9399033b4685
If you can't purchase a plan that allows DB larger than what you are using right now, then this problem will continue to happen IF you manually remove records in the DB without removing also the actual files.
Only way I can help is to tell you that - and to suggest (IF your time is worth anything and you desire to NOT have these problems) you purchase a plan that allows for larger DB's. If the provider cannot do that ... search for another provider.
Continuing to manually remove records and files leaves a lot of room for human error. One of these days you could end up destroying your Moodle site. Only hope and re-course is for the provider to restore your site. Uhhhh, your provider is taking snapshots of your space, aren't they? That's probably not a free service and will cost.
IMHO, this does illustrate that maybe Admins of a site do need tools inside the Moodle UI to 'deal with' the new file system. But, wouldn't expect any such tool from Moodle HQ coming anytime soon. Hasn't reached critical mass yet.
http://docs.moodle.org/26/en/Cron
Since you are remotely hosted, check with provider about how to setup cron jobs.
'spirit of sharing', Ken