Jira only supports Issue -> Sub-task. (Note that I'm using Jira-speak here - you can have many different names for the issue and sub-task types. Almost all of us have an issue type called "story" at the issue level. I'm talking about layers or levels here, not specific named types)
Jira Software enables Epic -> Issue -> Sub-task
You can then add Advanced Roadmaps, Structure, Jira Align, Big-Picture and so-on to enable more layers, but you'll need to think about how to map them all.
Yes, you can import fields from Redmine, as well as attachments.
There's no import of users directly, but you can tell Jira to create missing users from the issue data. If, for example, you don't have Bob as a user in Jira, but your import data has Bob as a reporter, assignee, authoriser, participant etc, Jira can create an account for Bob.
I would like to add only a few words about BigPicture. As @Nic Brough _Adaptavist_ mentioned in BigPicture/BigGantt, you can automatically create a no-limited number of WBS levels. Task Structure can be created based on both build-in task attributes (e.g., Epic link, Component, Version, Sprint) as well as links.
Even though stories and tasks are on the same level in Jira, in BigPicture, you can create a hierarchy similar to the one between epic-story.
Let me know if you have further questions.
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