How long does a comic take to write and publish?

It depends upon the company and the creative team.

Comics are normally monthly and will often feature the same creative team for several issues so it can be inferred that the turn around is one month.

However:

Writers often can write for more than one title a month. This means their turn around is anything from a couple of days to a couple of weeks.

Artists normally only do one comic a month so their turn around is probably 2 to 3 weeks (occasionally longer).

Comics are solicited 3 months in advance via Diamond Comic Distributors and retailers have to order speculatively in advance. This suggests that final editing and publishing take longer than a month.

Bear in mind that when the writer and artist are finished on one issue they move onto the next so several issues could be at different stages of development simultaneously.