When I look at my hosts list at https://www.boincstats.com/bam/hosts/
and I click the link '» Show all hosts ', on the bottom,
additional hosts show up in red. Even hosts that are still making points today.

Why is this?

Is this because they were passive for a while, and BAM thinks they're no longer active?
Or is it because they don't use a BAM manager?
Or is it because they're in some sort of group?

What would happen if I click the red 'x' next to it, saying 'delete this host', if the host is still active and giving points for the past weeks and days?

We don't know, because we're not BOINCstats.

Willy runs his own, third-party, independent, site. Ask on his own message board - he does monitor that (he replied and fixed a problem which I reported to him at the beginning of this month).