960px, (with or without a grid system) yes, is a good fit. The majority of screens out there are above 1024 or 1024 (wide. Actually 960 is due to the scroll bars, etc), 800x600 has become less and less (very low % according to my stats...) used, although smaller resolutions are being a bit more common for mobiles and handhelds, but is better to do alternate pages/systems for those devices, rather than sacrifice so much the design, IMHO. Some people though design at 770px, or something like that. We are talking here about fixed width pages, usually centered. But depending on the type of site, you could also do liquid layouts. phpBB forums are a good example of it.
use "slices". You create them with "slice" tool, is a "cutter" icon.Just be sure "Snap" is on, at "View" menu, and that snap to slices is on, there. Also that snap to document bounds is on. Snap to layer often becomes more a problem if ON, in my experience... You just draw you slices, and save the psd, so they will be allways there. If need to change layout a bit, change them also, use zoom to adjust to pixel. Zoomed in, you can adjust the margins of the slice, clicking everywhere on the margin. So if you export often with changes, this becomes more and more useful.
I don't understand this one.
They are not "informed"... You just decide what is it going to be. If it's going to be liquid, you can do an abstraction, set whatever size of the dynamic area, as that you will handle with code. Just use a usual width to make a visual idea as you work. And use sectors, again, using fixed width for the elements that are fixed (icons, etc)
Tips... Use Photoshop "Actions" when it has sense. So you will automate certain things. Work on the psd only for first drafts, in the brain storming stage. Code once the visual design is generally acepted.
Other tip: Don't use the web export code of PS. Just make the width of your elements as you need them, then put those widths and heights in your css classes page.
Edit: 3. I think you mean setting a div with a width and height of the exact content area , a slice of the whole header image, where your logo is. Give the div a background (by asigning to it a css class with that width and height, and background image) with that exact sliced chunk . You can redefine by css the
<a></a> tag inside that div, setting it to be display:block, having the exact width and height of the "hot area" , usually the logo, to link to home.html, for example.