When a question is about an OEIS sequence, it should include the name of the sequence (Axxxxxx) and a link to OEIS in the question body. When a question turns out to correspond to a sequence, the name and link should be edited into the question body. That deals with your three points:
- You could use the list to check if a question related to an OEIS sequence is a dupe.
Search for the name of the sequence.
- If you want a question idea, you can use the list to find potentially interesting OEIS sequences that don't have questions.
That's really the same point again, because finding potentially interesting sequences among all the not very interesting ones is the hard part.
- If you like a sequence you could see what questions have been asked about it.
That's certainly the same point again.
If there is an additional need to generate a list of sequences which have been used, I think that should be possible as a query on data.stackexchange.com, although I'm a bit rusty on string handling in T-SQL so I won't attempt it now.
This does also imply that we might need a site maintenance project to go through looking for questions which have links to OEIS in the comments but not in the question body. If you decide to do that, please bear in mind that edits bump questions, so with a project like this it's best to only edit about 5 questions a day.