1) I don't think that PPAs may be preferred 'over' core repos; instead, they should used in addition to core repositories when you need something different (i.e. latest Apache) that distro doesn't provide
PPA allows to install and upgrade software and track dependencies using same 'standard' discovery, installation and upgrade facilities as apt-get, synaptic, software manager and so on.
2) There may be compatibility issues, i.e. when I install PHP from PPA, I cannot install different version of PHP from standard repository. I can have only one product with the same name at a time.
If I have to install something really exotic, I would prefer building from source and installing along with distro-provided version on different path (at /usr/local and so on)
3) Usually I search for solution for some problem (i.e. install PHP 5.3 on Ubuntu that provided PHP 5.4) and and up with link to some PPA in someone's blog entry
PPAs are different in terms of how they are maintained (here the word 'Personal' in their name); some are less well maintained and some are maintained better. I would try and see which one can install on your system and work without a problems. Usually you should be able to uninstall software from PPA and return back to original packages, then try something different.