How to offset an EntityFieldQuery when using pager?
First question, you've asked if you can offset the results, without having to set the limit for the total results. Logically it would make sense to be able to set $limit = FALSE, to return all results. But I believe range($offset, $limit) requires you to enter both the offset and limit. A workaround is to enter range(3,9999999999);.

Second question, you've mentioned that the -range() is not working when -pager() is set. It's a known limitation. I would assume you can run a separate query to create a pager, but that would require additional SQL requests.