My problem was with the fogged up mirror after a shower. I tried some 'solutions' (spraying mirror with a fog proofing liquid, separate showering room etc) but eventually went back to shaving before showering

Antifog coatings from any scuba supply shop help, but one really effective method is just to aim a hair dryer at the spot you need clear. Not only does it get rid of fogging there, it prevents new condensation from forming because of the residual heat.

This. I shave with water and a mach-3. Have used this technique for over 25 years. Can't think of a time when I've had razor burn. I can't recall the last time I cut myself either. I even go against the grain at the end (people who witness this seems to cringe). I hate shaving and do it once every week or two though. I'm blessed to have very slow growing face hair. My blades last a really long time because they're almost never used.

Doesn't work at all with an electric razor. If I forget to shave and take a shower, I can forget to shave that morning.

Best time to shave!

I rarely use anything. And to be frank, when I do it is a small drop of hair conditioner.