I have a similar press in similar condition. I used it last weekend and the spots brightened up after using the press, meaning some of the exposed iron dissolved into my crush. I haven't noticed problems with this in previous batches. I don't know how much iron can be tolerated before it causes problems but from my experience, small spots like you show aren't likely to cause a problem. It depends on your risk-tolerance.
I have no idea about the potential risks or benefits of coating the spots with oil or lubricant. For myself, I'm squeamish about getting oil into my wine. If you try it, I'd be interested in finding out what you think.
Iron contamination can show up as haze in a previously clear wine. Or it can show up as a deposit at the bottom of a bottle of red. Either of these are cosmetic problems that should concern a commercial winery but it wouldn't cause a problem with taste. To test, put a sample in an open container in darkened and cool place for a couple of days.
Reference:
http://www.wineskills.co.uk/winemaking/winemaking-knowledge-base/iron
I have cleaned and re-painted areas of my press. Surprisingly, these areas have lasted nicely but some areas with the original paint are chipping and opening new spots for attack. I guess the problem lies with the manufacturer rather than the user. So, maybe the answer isn't powder coating but stripping and re-painting your press. Still, wear and tear will inevitably expose iron to your juice so an annual touch up might be necessary if you want to minimize exposed iron.
I used bees wax on the screw to act as a lubricant and to keep the exposed metal from contacting the juice. I don't think it hurt but it didn't help much either. The beeswax made a black sludge on the screw. I cleaned it off and don't do this any more.
Powder coatings can be food safe but you need to specify this with the shop that does the work. They sand blast before powder coating so you don't need to. You might want to dis-assemble your press ahead of time. And you won't want to powder coat the screw. The coating on the screw won't hold up to abrasion and might interfere with your ratchet.
To me, this is a worry but I haven't found it to cause any issues. The solution is to replace the press with stainless steel. I'll wait and see.