lol we probably need a Q&A thread but sure I'll just freelance these off the top of my head.
1. When the survey corps tried to capture the female type titan in the forest for the first time, how did they knew she would appear that day and follow them all the way to the forest?
They suspected the titan-shifters were after Eren and the whole point was to lure them out. There were some clues early on that the titans that attacked walls where intelligent and not typical titans as they targeted the gates at the walls specifically. Then later on they captured 2 wild titans that Hangji was experimenting on trying to communicate. Then those titans were killed by someone so they knew something was up.
In short they did a lot of Sherlock Holmes style deductive reasoning to come up with a hypothesis on titan-shifters targeting Eren. It's not that they knew 100% they simply took a gamble that if they went out to titan controlled areas outside the protection of first 2 walls that the titan shifters may appear.
2. Having wall maria breached, from where did the survey corps left? I am talking about the same day when they tried to capture the female type titan for the first time. The only logical answer I find is that they went all the way to Eren's home district to get deep in Titan territory through the hole the collosal titan did five years ago, or they never left wall maria?
Okay this does get a bit confusing so I understand but let me state that they have never made it back to Eren's home district of
Shiganshina in the manga yet otherwise Eren would have gone into the basement !
A - When the Colossal titan attacked
Shiganshina in the first attack years ago it broke the Shiganshina outer wall then
the Armored titan hit the wall between Shiganshina and wall
Maria letting titans into the
inner area so all the other towns connected to Maria even though their walls were up had to fall back as titans would be able to roam free and they would be cut off from the rest of civilization.
B - The distance from Wall Maria to Wall Rose is about 100 km so that is a lot of open
inner area now roaming with titans.
C - I think I should point out what was never stated openly but should be obvious is that the area space in between walls is what they use for farming and raising cattle/horse etc. thus is kind of the open farmland countryside. The districts are the cities where most people live.
D - The survey crops left from wall
Maria's Karanese District on the
east to try and reach
Shiganshina which is in the
south.
E - Remember the colossal titan appeared again in
Trost in the
South and attacked when Eren and them were still trainees but it disappeared shortly after appearing but left a hole whic
h Eren eventually sealed with a giant rock!! This is why even though
Trost is closer to
Shiganshina which is also in the
South they had to go to the
East district of
Karanese to reach Erens home.
3. What happened to the other 3 districts of wall maria after it was breached?
They evacuated as i explained cause they would be disconnected from the rest of humanity and certainly would starve cause the area behind them is roaming with titans.
However most of them are dead now anyways cause shortly after fall of Maria and everyone evacuated the government came up with plan to send out thousands of people to retake wall Maria. It was not expected to succeed but really the plan was to get rid of all the hundreds of thousands of people who they had no means to feed as all those people were crammed into the cities on wall Rose and they did not not have to resources to feed them.
