If customers make every payment their score should improve.
That's an incomplete answer because it doesn't take total debt burden and history of payments into account over time. Score is fluid and should decrease while debt burden is high or increases. At the end though, score should improve slightly because they are slightly more trustworthy having repaid what was promised.
Not if it shows a bunch of Affirm loans. You could look overleveraged for say getting a mortgage
We don't really know that. The algorithm is secret.
What is the benefit for a consumer to use this type of loan and then pay it back on time versus using a credit card and then paying the card back on time?
To me this seems like a new product that would target a different consumer than the one that makes payments on time. But I would like if someone challenges this view. Thanks!