Rational basis is essentially being able to articulate a legitimate government interest and stops there. Intermediate scrutiny steps that up to an important government interest and requires that the government action must be through means that further that interest. Intermediate scrutiny is commonly used for sex discrimination. Strict scrutiny requires a "compelling government interest" with the government action narrowly tailored to achieve that interest. Strict scrutiny is applied when basic rights are involved - speech, religion, etc.
This online legal dictionary runs through each of the review levels with some good examples.
Legal Dictionary Article on Strict Scrutiny
Yes, that is the way I have read it.
The Ninth Circuit, in Peruta, simply accepts the idea that restricting access to guns promotes safety. The ignored the fact that open carry is banned in California.