Yes you can
Yes
There are luggage racks. Personally, as this temporary Sky Club is very busy, I'd feel a bit skittish about leaving my suitcase(s) there. What I'd do if I did that would be to frequently go over and make sure they are still there. Question: Why not check your bags with Delta? Or if it's one carry on you've got, keep it with you while you're in the Sky Club? That is what most people inside there do!
Yes you can take your suitcase into the Delta Sky Club. Hope that assists.
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