Do units heal faster in your own territory? And what about when they are in a garrison?
That not exactly it. As pointed in answers of this question, units heal a percentage of max health each turn, friendly city and watchtower only give your units an heal boost.
- 5% is the default healing.
- 10% when your troops are on a friendly city, garrison or not.
- 20% when your troops are on a watchtower.
Also, some building, heroes, factions and quests can boost your healing. Again, see this answer.