Should I have both Transaction Log Backups and Log Shipping
You will only have one stream of log backups, and that would of course in this situation be your log shipping backups. If you keep doing log backups in your maint plan, then the log shipping restore will fail as soon as maint plan log backup was done "in between" two log shipping log backups. A: Remove the log backups from your maint plans. B: Yes, it does - it is a regular log backup, after all.