You can use a latex primer and I often do for projects like this because they are easier to use and do not stink, but be prepared for some stains that may bleed through the latex primers. You may need to spot prime those stains with an oil based primer. I usually have a few spray cans of Kilz on hand for this.

Really either will be fine. Most important is using a sandable product. I can't think of an interior oil product that is not sandable and they will kill any stains as well, if you go with water based make sure to check the can (wouldn't trust the guy at the counter on that one). Look for enamel undercoater and make sure it's sandable. Oh, remember to sand lightly after priming.

Some of the Sikkens products have considerable sheen. Existing transparent or semi-transparent stains don't normally need to overly prepared if not let go too long. It is important to occasionally give a "maintenance" coat when you see it start to show wear. You only need a primer under SOLID hide stains. All good paint/stain products have a mildecide in them. I am not sure how parafin affects the performance of stains. If the wood to be stained has never had a water based product on it, it should accept additional oil stain. If it has grayed with age, you can restore the natural color of the wood using a deck cleaner. You should remove graying, as it will show through a transparent or semi-transparent stain. Of course, if there is color from an existing stain on the wood, it too will affect the final look of the wood. Old color from a penetrating stain cannot be totally removed.

For that application, I’d consider a hardwax oil, but only if you want a matte finish. One example is Rubio Monocoat: super easy to apply (do all sides), and smells wonderful, but sand carefully/evenly and only to 120 grit (150 at most), or you’ll have trouble with adhesion. https://www.rubiomonocoatusa.com/pages/oil-plus-2c-colors