I’m currently working on the phpBB importer in order to fix some problems of the importer.
Regarding point 1: Are you sure those accounts are just disabled? This sounds like anonymous users which currently are not supported by Discourse. Disabled users should currently be imported as normals users, which isn’t correct either. I’ve fixed that in the version of the importer I’m working on.
Importing of avatars should work. I’m not aware of any case where it doesn’t. Custom emoticons are currently not supported by Discourse, but I’m not sure if converting them should be done by the importer anyway. Maybe configuring a custom set of emojis in Discourse will be enough when this is implemented.
That’s a tough one. I’m not sure how this can be fixed since the Markdown parser interprets it as a list. The current parser has quite a few problems with edge case like this. I guess we’ll have to live with it.