Hey Harry,
There is no standard in the games industry - some companies are very fast to respond and some take forever. The usual is about 4-6 weeks, I’ve found. There are a good few polycount threads on this page that will give you some extra information on this stuff. You could also search as it’s an often covered topic there too.
http://wiki.polycount.com/CategoryGameIndustry
HR can be understaffed in companies and, although it sucks, this can lead to no replies if you are not on their shortlist. Because of this, emails can be lost too - so if someone who has shown interest doesn’t follow-up - it’s okay to check with a friendly email. A lot of companies don’t always keep their websites up-to-date, so a position may be filled if it’s been around for a while (but don’t let that put you off applying!). However, you can certainly email them politely to check. Usually, if you’re applying for a position you can follow-up with an email after 2 weeks, as this shows you are keen (that is if it’s not an automated system rather than a email address).
The “acceptable” time frame between applications is around 6 months. Once again, there is no standard, but this is what I’ve read.
If you’re applying prospectively and there is no response - don’t harass. Nothing wrong with sending something in, but if there isn’t a position advertised for it you can assume if they’re interested they will contact you.