Summary is the only user-enterable field that cannot be left off an issue.
An issue also belongs to a project, is of a type and must be somewhere in a workflow (have a status), so although they're not really fields, I suspect they should be on your list.
There are some derived fields you can't get rid of - created, updated, creator, and resolution date are the ones that'll show up. Plus, your reporting won't work if you don't use resolution and if you choose to use some functions (epic links, sprints, etc) then some other calculated/display fields will appear.
Other than those, I seem to remember you can hide, or at least choose not to use, everything else.
Depending on where you're seeing this, it is mostly configurable (project type; team or company managed, and which issue view option you're using determine what is configurable here and how you get to it!)
The fact you've got "source" in there is a giveaway that it's configurable though - it's not a system field like the others, so if it were not configurable, you would not see it above original estimate and due date.
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