Dodgy analogy coming up...
When I eat at indian restaurants, they try to be helpful and tell me how hot their dishes are. Some use some number of chillis on the menu, and I always assume that the more chilli symbols, the hotter the dish. Others use mild/medium/hot in words. The chilli icons and words each describe a coordinate system. They describe how the hotness varies from dish to dish. Call the chilli icons, and the hotness words chilli SPACEs.
Now, at one restaurant, we can tell how hot a curry is. Each dish is given a value in that restaurants chilli space. (Analogy, the chilli spaces are like colour spaces, they basically tell you what units are used, and the range of hotness/colour.)
Now, the problem comes when I go to a new restuarant. How does the number of chillis used at the new one compare to what I am familiar with. Perhaps what I am used to as a 1-chilli dish at my favorite indian will be too hot for me at the new restaurant? Or too mild? The problem is that Indian restaurants are not calibrated one to another. The values they use are unique to their restaurant. Sure the units (number of chillis or mild/medium/hot) are the same, but you cannot assume that mild at one restaurant is not medium at another.
So, it'd help to have restaurants calibrated, so hot/3chillies meant the same thing everywhere. NOTE that this is independent of the chilli space.
Imagine we had a probe we could poke into each curry, and it would tell us some number that uniquely represented the chilli-strength. Now we can tell how each restaurant compares strength-wise - we have a calibration curve per restaurant. Each restaurant can continue to use it's own chilli space, but we can use the calibration curve to adjust their space into a common one. Back to the analogy, each output device (monitor, printer) needs to be calibrated to check that when it is told to output a certain colour, it actually does.
Onto your questions... Yes, I'd suggest that you keep in sRGB all the way. I fully expect that your printer and the other projector/computer can accept sRGB, can might well have been designed to only work with sRGB.
A1) Been a while since I played with lightroom, but I'd expect most of what you can do there you could do with CS4. Don't use ProPhoto unless you have a compelling reason to. (I suspect that you don't).
A2a) Do you need to save to jpeg for printing? Wouldn't think so. Perhaps you meant save to jpeg for projecting from the other computer? I'd choose my printer calibration from the printer driver, I'd select "Photoshop Manages Colors" and then select my printer profile from the Printer Profile drop down.
A2b) The photo will already be sRGB, so nothing to do here. You'd need this step if you did work in the ProPhoto workspace.
A3) Um, yes, make whatever edits you want in PS. Print the photo before you convert to 8-bit and jpeg. If you've gone to the trouble of adjusting things, why not save out the changes as a PSD for future use?
How I work is:
i) Open AdobeRGB RAW in CS4, choosing a 16-bit version from Adobe RAW.
ii) Crop/edit/whatever and save out a PSD.
iii) Print (telling the printer I am sending an AdobeRGB, and using the printer profile I have, as per my A2a above.
iv) Resize for the web.
v) Save out a jpeg, with the AdobeRGB colour space profile buried into the jpeg.
vi) Resize for a thumbnail.
vii) Save out a jpeg in a tn (thumbnail) folder, in sRGB and with no profile information.
I don't overwrite the PSD, so my steps iii onwards have to be repeated if I change my mind. These steps are really output-format steps, I have done the hard work at step ii.
Your mileage may vary. :-)