What is the general opinion among editors about whether my paper should be submitted to review to academics from the same University/department? Will this ever happen? If it does happen, isn't this bad for the quality of peer review because the reviewer might have a good relationship with the person who submitted the paper and may be biased consciously or unconsciously towards giving a favorable review?
Conflict of interest rules vary between journals, and some are far stricter than others. In general, it's not clear where to draw the line for what's appropriate. Asking someone from the same department to review their colleague's paper would generally not be done, even if no rule forbids it. Beyond that it's a little less clear, and you can make up all sorts of borderline cases. (It's considered fine for people from different University of California campuses to review each other's papers. What about someone from the Harvard biology department reviewing a paper from the Harvard medical school? I don't know, and it's not clear to me that there's a simple rule for deciding what constitutes a conflict of interest.)
Handling conflicts of interest responsibly is an important and difficult part of being a journal editor, since there are all sorts of relationships that are not as easy to detect as a shared departmental affiliation. For example, some people have been best friends since they were in grad school, while others may be enemies or rivals.
Sometimes when evaluating a submission it's valuable to get advice from someone who has specialized knowledge you need, but who also has a conflict of interest. In that case, you should be aware of the conflict and try to adjust for it (for example, by asking the person for objective information rather than opinions). By contrast, it's much more dangerous to rely on someone who has a conflict of interest you are unaware of.