Help!

1) If it's not in the Forge, you must buy the blueprint. In the Forge, you'll see where you can obtain the blueprint.

For Tenka Fubu, it's a F2P blueprint.
But for others like Kenshin (need to buy Kenshin to clear his library mission) and Masamune's (need to buy the IAP battlepass to be able to work towards unlocking the blueprint), you cannot get them.

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2) Players have up to 5 sweeps a day in total (depending on Tenshu level).

For Library, a hard mode story allows 2 sweeps to be consumed per day, while you can use 3 sweeps in normal mode.
For Expedition, you can spend up to 3 sweeps for any one.
In Training Ground, might be 1, 2, and 2, or 1, 2, and 3 in ascending order of difficulty.

This means you can use all 5 sweeps on 2× Masamune Hard, 2× Namioka, and 1× Advanced Musket Training, or 2× Masamune Hard, 1× Ujiyasu Hard, and 2× Namioka.

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3) As in Siege of Takato Castle, Takeda Clan playable mission 6-4? Probably don't defeat the ranged troops and let them attack the castle garrison from afar. This prevents enemy reinforcements from showing (assuming the trigger is defeating all accompanying troops).

Alternatively, you can consider pulling all troops back to the main castle and settle in for a siege. Not sure if losing the branch castles will give an enemy additional advantages.

If I understood you correctly, you have Akechi Mitsuhide as your best gen and/or only gold gen. He would be useless because you cannot deploy gens.
If you have Mochizuki Chiyome, deploy her on your best ranged unit, or remove the unit given to her (she would probably spawn with ranged ninja). Give her your best equipment.

If you cannot win with at most 5 normal and 5 large food, just give up and return much later.

1. Achievements, daily Missions and boss fights in Expedition, as well as daily sweeps of cleared Expeditions. Otherwise, Challenge Conquest and conquest achievements.

2. Not sure about how to fix that. Assuming that you enter the game with a stable internet connection after the reset time, you should be able to use up your daily sweeps. Otherwise, level up your Tenshu.
For Expeditions, I meant sweeping a cleared Expedition, not pressing the <Sweep> button instead of the <Enter> button to clear it.

3. Oh, you meant the Battle of Tenmokuzan in Campaign mode, not the Legendary Takeda Clan mission. You can search this board for the guide.
Basically, take Shinpu, sent troops after the SE city and Katsuyori's forces. Not sure if the escort mission is in Normal mode, but this requires you to escort the target to the respective circle to get the Sanada clan to defect and join you.

4. You get war souls from rolling the gacha. To exchange, tap on the <Recruit> icon, then tap <Exchange> at the bottom left. Lastly, pick the gen and the number of fragments you want.
Use the souls wisely.

5. Daily invasion, clearing campaigns and other missions (even repeat clears of already cleared ones contribute a little), conquest runs, clearing Expeditions, sweeps, and selling junk.
Plan wisely.

6. Ieyasu's set is F2P but very expensive. Usually the 2-piece sets are also F2P. Otherwise, there are incomplete sets. There's a thread in the board, but it probably has not been updated to reflect the newest equipment from the invasions of Joseon.

7. Training Ground is in Joseon and is way too expensive and far for you. Focus on conquering all of Japan in Tenkabito first. Your income is based on the number of complete provinces held.
Daily Invasions will occur after possessing a certain number of castles.

8. Don't upgrade based on who you have and their special units. You can ask around about the best units based on what you have. There are many good ones, like the mounted archers and teppo, as well as akazonae cav for the ability to attack again after destroying an enemy. Samurai Warrior(?) has the best atk statuses out of all Japanese inf units, probably. Destroyer of Provinces has splash effect while Mortar probably has the best single-target statuses against land troops.