With Minewatch 3.12:

• Healing cannot be dispensed to teammates (from any hero) but upon removing them from my team, I can heal them.
• I also cannot heal myself, whether it's as Lucio or with Moira's heal orb

It sounds like your team has friendly fire on (which is default if the team was created via commands or in an earlier Minewatch version). You can disable that with /scoreboard teams option <team> friendlyfire false.

There is currently a bug with Lucio and Moira not being able to heal themselves while on a team with friendly fire enabled; that'll be fixed in the next update. Thanks for reporting it!