Hi Mara,
Office 365 has been transitioned to SharePoint 2013 in the US. Are you saying it's still SharePoint 2010 in Europe?
Office 365 is a very limited environment for InfoPath browser. Are you experiencing the issues int he browser or in the InfoPath filler?
Have you tried to call Microsoft Support?
SharePoint 2010 standalone environments do not have as many limitations and in general they can be worked around via Central Admin. Unfortunately, O365 does not give you central admin.
There is no defined max attachment size. We have customers with large attachments in both browser and filler. There will be timeouts submitting if the bandwidth is low and/or if the image is very large.
Good luck!