"Stand by your man" is the name of a famous song (Tammy Wynette?). "Stand by me" is another one. It isn't just regional. "They stood by me when the going got rough" or "They stood by when the game got rough" are common comments. "They stood by and idly watched as the bully stomped the bystander" would be a legit comment.
Do try backing up your claims with some evidence.
Check the first meaning of "stand by someone". Although it's not the only meaning of that expression, it must be listed as first for a reason.
P.S. Here is more: http://www.oxforddictionaries.com/definition/english/stand-by?q=stand+by
Your sentences sounds like motion is implied, i.e. 'I stood by him on purpose' = I placed my body near his with my two legs versus 'I was standing by him when the bomb exploded' meaning maybe he stood by me but it's not really important who placed their body in that position. Position versus motion basically.
Can someone tell me if this is right?
Стоять / постоять - to stand, to be standing, to stand (for some time)
Ставить / поставить - to stand up (someone or something)
Становиться / стать - to stand up (one's self), to become or begin something
Встать / вставать - to get up, to stand up, not really sure how it's different than становиться
Different languages merely have different concepts how to express things, tenses are no exception. In my native German for example we need context to differentiate between "stands" and "standing". (same goes for most of the past tenses) Often the information is not necessary and is omitted altogether, otherwise we would add words such as "usually" or "right now". (using the correct time in English is really hard for many non-natives) Russian has perfective and imperfective words, but I'm sure that's not enough to solve the "tense problem", so they might add the same approach.