I agree with @Smurf2 on this.
I tried to keep my original answers brief because going into detail risked confusing the original poster even more than he already was.
The main reason for the 300-ppi rule of thumb is, first, it’s a good, round number that people can remember and, second, it provides some wiggle room to work with the photo when placing it into the layout.
I’ll state again, though, that 150 ppi is way too low for standard-quality offset or its digital equivalent. By that, I’m referring to instances where a more-or-less standard 150-lpi halftone screen is used. As already mentioned, the lower the lpi is, the lower the ppi can be. At a newspaper where 85-lpi halftones are common or on billboards where the lpi can get down into single digits, the ppi can be reduced proportionately.
For a high-quality photo meant to be seen at arm’s length, printed offset on good paper, the resolution should be no lower than 240–250 ppi or it risks compromising the detail in the photo — especially when the photo contains lots of sharp detail. Even then, lots depends on the photo. An intentionally blurry photo with few sharp detail can look perfectly fine at even lower resolutions.
Yes, if I understand your question correctly, you got it right, but as already mentioned, the photo doesn’t need to be 300 ppi. Assuming a halftone frequency of 150 lines per inch, you can get away with resolutions down to around 240–250 ppi without being concerned. What won’t do any good (in most instances) is upsampling the photo to artificially boost the ppi — that just stretches the existing image across more pixels without accomplishing much of anything.
If possible, and if you’re still doubting the results, as Smurf2 said, ask your printer. However, that’s sometimes not practical.
The newspaper where I worked printed the daily paper at 85 lines per inch, so we sampled all the photos to about 170-ppi, which gave us some wiggle room to resize the photo in the layout. Realistically, without doing the math, 140–150 lpi would likely be fine. 240 pixels per inch for newspaper work is overkill.
I can almost agree. For someone in a tight spot and where the photo isn’t that good to begin with and where nobody will be paying much attention, the lower resolutions you mentioned likely won’t be noticed. I’ve done it myself when needed, but only when other options aren’t available. I’d not be inclined to call it “absolutely fine,” though — especially in those instances where the photo will run large and, as Onion_5 put it, the “original is quite nice and sharp.”