For the computer and generator question, I think it would be fine as long as you operate the computer of an UPS (uninterupted power supply). This will ensure you get steady power to your computer, but will also protect against unwanted shut downs if the genny splutters out of fuel.
There are different types of UPS units that use different means of regulating the power output. Not being an electronics engineer I have no idea how this works, however I imagine there would be at least one type of UPS that would be preferred for this scenario.
This post:
http://it.toolbox.com/blogs/it-guy/generator-ups-wtf-15939 would seem to indicate that highly specialised knowledge is required to get it right!
This article:
http://ecmweb.com/news/electric_ensuring_generator_ups/ seems to confirm that.
A power conditioner may be preferable to a UPS in this scenario.
http://www.practical-home-theater-guide.com/power-line-conditioner.html