(Rough) camera calibration of manipulated images
1) It seems to me that you don't care about solving for correspondences or obtaining any high level paradigm in that sense. So I would treat this problem as a minimal problem and redirect you to check:

http://cmp.felk.cvut.cz/minimal/

Maybe specifically, 4-point method with unknown focal length:
http://cmp.felk.cvut.cz/minimal/p4pfr.php

You could find many variants in that page.

2) Well, this problem involves many issues of multiple view geometry theory. However, in this case, an uncalibrated approach would be more suitable.

You could obtain point correspondences from SIFT-like features. As your images are downloaded from social platforms, it is likely that they will contain a lot of such feature points. Then, you could match the descriptors in a RANSAC-like fashion and retain the correct matches. From there it is possible to compute $F$ the fundamental matrix. With further assumptions, constraints or knowledge about the scene you could compute the scale as well as  the 3D point coordintates. Some examples here:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.4741&amp;rep=rep1&amp;type=pdf

Under certain constraints it is also possible to recover the camera matrices:

http://users.cecs.anu.edu.au/~hartley/Papers/eccv92/Higgins/higgins.pdf

After all, I would recommend you to read:

http://www.robots.ox.ac.uk/~vgg/hzbook/