When should we use publication list for peer evaluation?
Q0. Short answer, all kinds; from trying to dig into all details you mention in your backgroudn text to simply looking at the number. My experience says that evaluations often have lofty aspirations but when it comes down to actually performing the evaluation, a time crunch or other circumstances makes evaluations boil down to simple statistical measures.

Q2. The short answer here is, we do not know. In order to say that one approach yields better results than any other we need some form of comparable materials. I have not seen such comparisons made (which of course does not mean they do not exist).

Bibliometricians work with more advanced tools to try to work out comparable numbers. Having been through a few such processes, for organisations not persons, I can say that the results often indicate whether the object is good, average or perhaps poor and not much more; very relative terms. In my experienced studies the litterature is dealt with after having been subjected to, for example, field normalization since different fields have very different publication strategies. This i sone reason why a straight IF or h-index has limited value; it is important to know with what one is compared.

Q2. What immediately comes to mind is funding. If one is looking for a person that will contribute to a department through their activity, looking at their publications may not reveal the whole. Ability to attract funding may be equally important. It is obvious that the two may be well correlated in many cases and really poorly in others so even this would not be straight forward. Again, one has to look at the norms for the particular field to see how these can be used.

Q3. Thhis goes back to my answer under Q2 to some extent. I think, however, that in order to successsfully select a person for a tenure track, one has to be very clear of what one expects from such a person. Looking at publication rate is one thing but let's say that person locks themselves into a room and is never seen except whena new paper is published. Is that what the department really was looking for?

Appointing (good) people (contributors) is a difficult task and I very much doubt that using simple tools is the best way. Surely some tools such as IF end the like can be used to narrow down a larger group but the smaller the group from which to select, the more obtuse such tools become. I believe multiproinged approachs where the search criteria are clearly identified from the beginning and followed up by an assortment of means is the way to go. This usually involves interviews etc. to figure out how a person can and will integrate and contribute to the work environment.

So the short of it is that you get what you deserve if you use simple tools and underestimate the effort that is needed in the recruitment process.

This answer is very relative, I know, but I am convinced that hiring people is so much more involved than what simple statistics can resolve.