How does the COVID-19 crisis affect durations of peer review and editorial handling?
I am an associate editor for two journals, and although the situation is fairly new, I expect to have no substantive change in the time for me to handle papers.

The reasons for this are:


Pretty much everything is handled purely electronically anyway, so there's no physical interaction to be disrupted.
Reviewing is typically a sparse activity by people who are mostly always overloaded anyway, and it's always fairly low triage for people.  As such, I don't anticipate the availability of reviewers to particularly change: if people have more time, they'll fill it with things more important to them; if people have less time, I'll just have to ask a few more to find a full reviewer set.
The time to review is typically dominated by the time that a manuscript ages quietly on the reviewer's desk before the review deadline arrives --- actually carrying out a review often does not take all that much time, by comparison. The number of weeks we give our reviewers isn't going to change, so that dominating time won't either.
Because of the preceding factors, there's already a lot of stochasticity in time to review. Even if it does go up a bit, I doubt it will be readily detectable against the background of stochasticity.