There is no information about the Sanctuary Gate and where to find the Engineer's Mansion. If you know where to find it, please let me know.

To open the gate, you need to perform a ritual in three places on the map (they are marked with a glow from above) with any hero - pay 15 crystals, and the gate will open. After capturing the castle, a teleport to Mukao will open.

I can't help you with the Engineer's Mansion, as I didn't have it in this mission.
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I decided to replay the game. Oh, these Nagas and their ability to run on water... They outsmarted me a couple of times and recaptured two castles on the water.

Overall, the mission is not difficult; the main thing is to fend off Kalindra's attacks at the beginning and quickly capture three castles - one in the east and two in the southeast on the water. By the way, I advise you to capture them before the end of the turn and before the end of the week so that a player with a strong army doesn't teleport there. Then, march to the castle in the center, sail on a ship to the path (don't forget to capture two forts there as well), and that's it. The map is at your disposal, and no one will bother you. You can calmly clear it, visit various upgrade locations, and collect bonuses.

Regarding Anton's development: if you are playing as a Warrior, then upgraded Reinforcement, Counter Strike, Cleave, and Endurance are essential. These skills will help you a lot. The favorite target for enemies is Griffins. I did this: I put Reinforcement on the Riders, and while the enemy was attacking the Griffins, the Riders eliminated the stacks, of course, with the help of Light Mages and Archers. Then, I resurrected the Griffins with Vestals, and that's it. You can also put Reinforcement on the Griffins, so you won't have to heal them, but I really like the horses ^_^ As for artifacts, try to equip Anton with items that increase luck, initiative, and morale. This helps a lot in battle. Have a nice game, everyone!