I think I have answered your questions below
"One thing that bugs me (or I can't figure it out) is how
to use the metering system so that you can see what aperture and speed
it wants to shoot at before you shoot."
I only use my S70 in "M" (and saving in RAW) so M first, then Av.
I assume you've set the display mode (display button toggles it) to one that shows something on the LCD.
M - mode.
If the LCD tells me I'm way off, I adjust the shutter speed until I like what I see. The numbers displayed at the bottom of the LCD are your choices. The info on the LCD - the number at top left when you half press the shutter button - is the difference between your choice of shutter/aperture and the suggested exposure in EV units (-2 to 2 in 1/3 EV). Note it only reads once each time you half-press the shutter (to do with the exposure lock function in Av mode, see below).
After the first exposure I look at the histogram (display button in preview mode allows this to be shown). If you have strongly-saturated, bright areas take care, but otherwise it should be filled nearly to the right side.
If I got it wrong I adjust. All other exposures under the same light are then straightforward - the same!
I nearly always set the aperture to f4 when I switch on the camera (i.e. at 5.8mm focal length) and let it drift to f5.3 on the last 3 steps of the zoom - I find that gives good quality and reasonable depth of field in all cases, but then I use other cameras for subjects where that is inappropriate).
Now I will try Av mode. It tells me the suggested shutter speed on the LCD (the number appears after half-press of the shutter button, and is locked until the button is released). It is to the left of the aperture value which is always displayed in this mode (if the display is on). If I find that the exposure is not what I want I can use the FUNC button to access the exposure compensation. After trying that I find that M is easier! Some people like exposure-lock, but I prefer M (on all my cameras).
"There are some other related items that I'm confused about.
I'd like to know how I can use the inbuilt light metering system to give me readings of highlights and shadows so that I know ahead of time what the difference in light
readings are within my picture and what settings will be used."
Point the camera at highlights, take a reading in Av, point at shadows, take another reading? Not sure what you want here.
"For instance in RAW or JPEG, outside, it kept using 1/1000 of a
second and just changed the aperture, consequently blurry images (lack of depth of field) when aperture was at 2.8 for a landscape shot with foreground and
background. And I don't know this information before I take the
picture. In the above scenario, I was in Program mode on the dial."
My dial will never go to P mode, even for you! I suggest Av mode for this
purpose (Back to M, tape back on to hold it there!)
Wow, I forgot I had f2.8.
"If I set it to aperture priority mode, then how would I know
what speed I'm about to use before I press the button?"
See above. If it does not show up on the display I do not understand what you are doing - I cannot avoid it on mine if the display is on at all.
EV - exposure value (equal to lens stops or factors of 2 in shutter speed).