I would not advise reducing the seatpost, nor widening the frame's ID. A close fit is a good thing for a seatpost.
Instead, clean the seatpost using your preferred solvent, and allow to dry. If its not smooth, a very light buff with medium/fine sandpaper would help, but you're only taking off the bumps.
If the post has nicks or damage, then you may need to do some localised hand filing and then sand smooth.
As for the steel frame, it likely has iron oxide in the seat tube, AKA rust. I would start by using a small ball of rag or a cotton ball on a stiff wire, to "paint" the inside using a rust reformer. I personally use a Phosphoric-acid based product called "Rustbuster" but there are many other options.
Your aim here is to chemically inert the rust, and replace it with a more-stable oxide. Do note this stuff will dull paint, so wipe up. It will also dissolve your skin, so gloves, and use it outside, with eye protection.
I'd lay the bike on its side and work the inside of the tube. Then flip the bike and do it again. This should minimise chemical getting down onto the bottom bracket and bearings/races. If you have a cartridge BB, this is much less of a problem.
Leave the product to cure as per label - mine takes anything from an hour to a day depending on how thick the rust is. A bike tube will only have thin rust.
Then get a suitable 10mm or 3/8" wooden dowel, and cut a slot in the end. Slip a piece of folded sandpaper in so that as you twirl the down in your seat tube, the abrasive rubs the inside. Mount the other end in a drill chuck and "whiffle" the inside of the tube while moving the sandpaper back and forth. It won't take much. Then give the tube a clean with some air or tap it upside down to get all the dust out.
On refitting your seatpost, use grease or similar. I have a copper/clay based product that works well, and repels water too. You only need a thin layer, and only as far up the seatpost as will go in the frame.
Prevention Often I've found the reason for seatpost corrosion is water in the wrong place. The two ways water gets there is either
- Rain/road spray/fog/sweat/etc dribbles down the outside of seat post and wicks down inside the collar, and/or
- The bike has a slotted hole in the rear of the seat tube for the clamp to compress. This slot collects road-water thrown up by the back wheel, where again it wicks into the joint. This is worse if your area uses salt on winter roads.
Mitigations could include fitting a rear mudguard/fender, reducing water ingress by adding grease to the area, or fitting a short piece of old inner tube over your seatpost and then down over the interface to the frame (once your saddle height is dialled-in of course.)
