I am a European, female working in a Japanese mid-size company in a director role.
Overtime: yes, there is overtime, but it depends on the project. I have previously worked many years in Spain and some years in Germany. I would say that overtime in Japan isn't that different from the situation in Spain. In Germany (and probably some other more Nordic countries) there is more a culture of finishing work at 17:00 and have little overtime.
Is overtime paid?, this depends, similar to the situation in Germany and Spain on your level of contract. In my position, no, overtime is not paid, but I also don't need to be at work at 9:00 precisely. This was the same in Spain as well, and if I'd be working in Germany (or the US) would also be the same.
However yes, our secretary, her overtime is paid, each single minute of it. There is a time registration system that records exactly when you come and leave and if you have a contract not at a manager or higher position, your overtime hours are paid. As Uco said, there is a law for that.
Being moved around (= Tenkin): I have seen some people at our company being moved, but again this was at a director level. I have the impression that at these levels this is the same worldwide. But yes, there is an expression in Japanese for Weekend marriages because sometime men (normally not the women) would get moved by their company and just get home on the weekends. Women (with children) would normally stay were they originally were... and frequently men would take up a concubine at their new location... (but well, these same men might have a lover in their home town too).
Contact lenses: no, in offices I wouldn't say that there is any policy written or not, against glasses. There was a story in the news a few months ago about some shop or so, that required contact lenses, so that's where you might have gotten the idea from. But no, I wouldn't say that contact lenses in Japan are more common for women than e.g. in EU, where they are also quite common. (Something I never understood, as I really like my glasses).
Hair dyeing: you didn't ask, but actually there is a policy (probably not written) against dyeing your hair. I.e. until a certain shade of brown it is acceptable, but blond (unless obviously you are a foreigner and naturally or even dyed) blond, is generally not acceptable. I don't think this policy is written anywhere, but de facto, you see very few women with blond dyed hair. And the ones you see are either students or work in very relaxed environments. Obviously black dye is okay. And some men, even in the business environment, are dyeing their hair in a very questionable red to try to hide their grey hair.
High heels: well, actually in the office most people wear slippers, often quite old ones. But yes, for client appointments very neat clothing and this MAY include for women high heels is frequently seen. I personally never wear high heels and would feel even stranger, as I already tower above most of my colleagues (just having average EU female hight probably). But again, there is no written or un-written rule in my company about heel hight for women. It just kind of comes with the business attire. Not so different from places like Spain/Italy, where business attire is also more formal in general than in Northern Europe.
Tattoos or piercings: Tattoos are generally very much frowned upon in Japan, and many places (beaches, onsen) don't allow you to enter with a tattoo. So yes, if you would have a visible tattoo, that would be a major problem in a Japanese company. This doesn't mean that no Japanese has tattoos. Just saw a lady in a sento last weekend, but it is really rare. I think in about 5 years of going very regularly to onsen, I have only seen 2 ladies with a tattoo.
Piercings, is pretty much the same and seen very rarely. (I am actually not even sure about ear piercing. I am trying to remember now... but I would say it is much less common than e.g. in Spain, where most baby girls get ear piercing within a few days of being born!) I am pretty sure this doesn't happen in Japan. But I guess that a small pearl earring would be acceptable, but it isn't really common.