Not to put too fine a point on it, but to answer the topic line: yes, there will be recurring problems. That's a consequence of the free hosting environment. There will always be idiots clogging up the outgoing mail queue, filling the server data store to the cutoff point, and hammering the database servers into submission. Some will be people who don't know what they're doing. Some will be malicious idiots who know exactly what they're doing, and only need to have an account last a few minutes or hours (before it's suspended/disabled) to accomplish their goal. Because there is no money ventured and no accountability, both groups are free to (occasionally) put the servers into a state where other people's sites are affected.
If you're actually doing anything that could be considered "mission critical", then Free Hosting is the wrong choice for you. It's meant for hobby/personal sites, not for business or brand presence. The paid option is far from expensive, comes with an SLA (service level agreement), has far fewer accounts per server (giving ore resources and less competition for them) and attaches financial liability to abusive accounts. If you are expecting commercial-level service and availability gratis, you're living in a dream world.