Best Format and % for Web & 4 Color Printing + changing DPI

I would say use Native PSD files  for placing in InDesign documents  and save as JPGs without much compression for distribution to others for printing and making photoprints. The difference in quality between TIF and JPG is imperceptible but the size of JPGs is much smaller. Save compressed JPGs or PNG for use on Websites etc. Keep your images in RGB color mode.

R-Photoshop  wrote I have heard the best format for web is JPG but what quality% is really needed for high quality photos like luxury home photos when trying to keep file sizes reasonable for faster viewing without loss?

Probably around 75%, but it can depend on the content of the image. Check out the following page, which lets you compare what different types of images look like under various JPEG compression settings. Find an image on the page that's most similar to yours, and then use the controls to interactively see how different quality levels affect appearance and file size. The page is for Lightroom, but applies to Photoshop even though each application uses different numerical scales.

Jeffrey Friedl's Blog » An Analysis of Lightroom JPEG Export Quality Settings

What you don't want to do is use 100% JPEG quality. Above around 85% your eyes can no longer see the difference, but the file size goes up dramatically.

R-Photoshop  wrote I cannot find anyone agreeing on the best format for sending a file to the printer for 4 color separation, I have heard JPG is not the best.

The disagreement is probably because it depends on the specific workflow being used. Photoshop format and TIFF format are generally preferred. Choosing between those, the specific workflow matters again; for example, if the print designer wants to be able to turn on and off layers of a Photoshop file from within Adobe InDesign, then Photoshop layered format must be used.

I agree with everything D Fosse said, with one addition. While CMYK has been the standard for prepress workflows, more are now RGB-based where the conversion to CMYK is done later in the process (such as at the RIP). If your printer is using such a workflow, they will tell you to leave the images in RGB mode. If you're printing on your own desktop printer, it will probably expect RGB images and will convert to the colors of its specific inkset in the printer driver.

Both questions have the same general answer: Figure out what workflow is being used for your photos, and that will lead you to the specific answers.

Oh, one more thing: if you're sending out CMYK for print, you must know the correct CMYK profile to use. Ask the printer. There is no such thing as a generic CMYK. Don't trust the (arbitrary) Photoshop default, chances are it's not the right one and it certainly won't be if you're outside North/South America.

Keep your master files as PSD or TIFF, then save out copies for web or offset print.

Ppi (pixels per inch) does not apply for web or screen viewing. The image pixels align to the screen pixels of whatever screen you're seeing it on. You decide on an appropriate pixel size, traditionally around 1000 - 1200 pixels long side. This fits comfortably on most standard screens.

Jpeg is very effective for web use.

For print, the ppi value comes into play. There is no pre-existing pixel grid on paper, as there is on a screen - so one has to be invented. This is the ppi number. It defines the printed size of the pixels in your file, how many of them to an inch of paper. In other words, pixels per inch. It's just metadata, not a property of the file.

For good print quality, you need a certain pixel density. For most book and magazine print, the rule of thumb is 300 pixels per inch. This determines how big it's possible to print your file.

Jpeg should be avoided for print because the aggressive compression is damaging to the file. TIFF is preferable and accepted everywhere.