I think 'let stand' is the standard phrase in written recipes, as in #4. 'Let it sit' is equally possible in conversation.
'Rest' doesn't sound as idiomatic to me for food, though there could be some AE/BE difference.
If it doesn't have mayonnaise, only vinegar, it doesn't need to be refrigerated/chilled and can indeed be served warm or reheated to serve.
And yes, one of my recipes for 'German-style' potato salad, from Heloise,* makes the dressing with (IIRC) chopped bacon (retaining the fat), chopped red onion, flour, celery seeds, cider vinegar, chopped celery leaves, and sliced radishes. Very tasty and can be served warm, room temperature, or cold. (-: