for the standings, dont worry on each corporations standings (companies)!
use faction standings. for instance in this guide Slav gives a list of corporations to use, one that seemed to raise quickly was Ytiri for me.
even though Ytiri is decent standings, im going based off of the Caldari standing. soon as you have the minimum for Caldari, you can then do that level mission for ANY corporation that is caldari based. it is MUCH MUCH easier than getting each corp standing up.
not sure about second part, so will have to wait on somebody elses response there

GL