How many manuscripts should I agree to handle as an associate editor?

I would start by asking the journal rep how many manuscripts (MS) other have agreed to, or what is typical. I would think that is what the journal reps would consider "normal". You probably have a sense of whether they need you for something very specific, in which case a lower number might be quite acceptable. Once you know what they tyically load on their editors, you should think hard about whether you find the workload acceptable. There is usually no guarantee that the workload is evenly distributed unless all editors are able to handle pretty much all submitted MS.

As editor you will likely need to at least browse the MS when you receive it, chase after persons willing to review, read the reviews and the MS carefully to provide feedback to the author, review the authors revisions, poissibly run the MS around again and then make a suggestion or decision on accept/reject. All this is within some time frame and chasing late reviews and authors who do not return revisions will take some time. I can also add that it will be the problematic papers that will take up most of your time, the good ones usually are not difficult to handle. You thus do not know how much time you will spend on any particular MS. A really good one could take half a day in total; a poor may take at least a day or more. So having slightly scared you with this, I will add that the work also has potentially tremendous rewards (reading brand new research and getting in contact with new persons).

So, in short, how many MS per month is really impossible to answer, it will strongly depend on how you feel about the work and how you think you can accommodate the workload in your own time. I will leave you with this slightly unsatisfactory answer, but urge you to try to get a sense of what the journal expects and what they consider normal. You could also ask to how much time they think the workload corresponds.

This varies wildly. It depends on the journal, how many submissions it receives, whether it has a full-time Chief Editor, whether it has one or more senior Editors below the Chief, whether Associate Editors receive any payment, and whether your subdiscipline is a popular one.

I'm an (unpaid) Associate Editor for two journals. For one, I handle about 6 manuscripts per year, for the second, I have been an Assoc Editor for 6 months so far and have yet to receive any submissions (it's a new journal so it isn't receiving many yet, especially not in my subfield). A colleague is an Assoc. Editor for another journal, for which she receives a substantial honorarium, and she handles 15-20 manuscripts each year.

The only way to find out is to ask the Editor who has invited you to join.