If I scourge a Shaper rare item and then use an alchemy on it, will it get a Shaper mod again?

Same for an Elder item. Does crafting on Shaper and Elder items remove the fact they're Shaper and Elder items (other than the artwork, which still remains)? Does using a scourge and then an alchemy (or just a Chaos Orb) keep a chance of the item rolling with Shaper/Elder mods? Or will the item always have a Shaper/Elder mod, so using a Chaos would always keep one of those mods?

items will not lose the status. they will roll the mods from whole affix pool. So you will not always get shaper/elder mods when rerolling it

They keep their Elder/Shaper base regardless of scouring or chaosing.
Affixes will be generated from a larger pool, containing "shaper" or "elder" ones, but not guaranteed.