Hi Alaray,
If you want to learn more, you can search for Late Bhante Punnaji in youtube about “Paticca Samuppada (Concise) by Bhante Punnaji”, my understanding and experience fall inline with his explanation.
Note: You may need to hear many times to get what he is talking about. Also don’t look at the figure, look at/hear the teaching if you want to improve. See if it is fall inline with your practice or not. If not, you can certainly throw it away. Likewise for my explaination below 
Q1
Cognition of outside environment (contact) is condition for feeling.
→ When you use your 6 senses to cognize the environment (contact), then internally/subjectively in your mind arise a feeling of pleasant, unpleasant and neutral.
Q2
Regarding the suffering and craving we experience, nothings are yours. They arise because of the 12 conditions hence dependent origination.
The suffering arise because we think “wrongly”, hence there is a satipatthana (Samma Sati step 7, bring your mind to within / introspection) to “correct” our way of thinking (dhammanupassana - last step of sati). I can explain further, but maybe too much for details.
My understanding about Anatta, you need to have a very clear mind, possibly 4th jhana to analyze the Panca Khandha (for freedom with wisdom as an arahant, or something leftover an Anagamin) or go up to 9th jhana (sanna-vedayita nirodha, SN 41.6) to understand there is no mind (completely stop the mind activity) and only a body (like death body). One who can reach this state and fully understood the whole links is known as freedom by 2 ways.
Q3
Free mind means entering a 1st jhana, etc. From sutta about jhana (ex: DN 10), Having withdrawn from senses desires, and evil states of mind, one enters the First jhana…
Note: It is not easy to enter a jhana, you need to have a perfect morality (consciously), and right understanding/view as the foundation.
For Dependent of origination, this is how my current understanding
Again, please investigate, my translation is different from common translation.
‘When this exists, then that is present; When this arises, then that arises. When this doesn’t exist, then that is not present; When this ceases, then that ceases. That is:
-Unconsciousness is a condition for Process Constructions Activities.
-Process Constructions Activities are a condition for perception.
-Perceptions are a condition for Constructed Entity and Identity.
-Constructed Entity and Identity are a condition for Experiencing Six Sense fields.
-Experiencing Six Sense fields are a condition for Cognition of outside environment (Contact).
-Cognition of environment (Contact) are a condition for feelings.
-Feelings are a condition for Emotional Reaction of feelings (craving).
-Emotional Reaction of feelings (craving) are a condition for Personalization of the Subjective experience (clinging, making subjective experience as mine)
-Personalization of the Subjective experience are a condition for Coming into existence imaginary “self” in an imaginary “world”
-Coming into existence are a condition for Birth (past).
-Birth (past) are a condition for Aging (present) and death of the body (future) as well as grief, lamentation, pain, depression, and exhaustion which start this existence in the world.
That is how this entire mass of suffering originates.
-When Unconsciousness fades away with nothing left over, with no emotional desire, and cease, then Process Constructions Activities will cease.
-When Process Constructions Activities cease, then perception will cease.
-When Perceptions cease, then Constructed Entity and Identity will cease.
-When Constructed Entity and Identity cease, then Experiencing Six Sense fields will cease.
-When Experiencing Six Sense fields cease, then cognition of outside environment (contact) will cease.
-When Cognition of outside environment cease, then feelings will cease.
-When Feelings cease, then Emotional Reaction of feeling (craving) will cease.
-When Emotional Reaction of feeling (craving) cease, then Personalization of the Subjective experience (clinging, making subjective experience as mine) will cease.
-When Personalization of the Subjective experience (clinging, making subjective experience as mine) cease, then Coming into existence imaginary “self” in an imaginary “world” will cease.
-When Coming into existence cease, then Birth (past) will cease.
-When Birth (past) cease, then Aging (present) and death of the body (future) as well as grief, lamentation, pain, depression, and exhaustion will cease.
That is how this entire mass of suffering ceases.
Apologize if I miss somethings. Teaching of buddha need to be listen carefully with clear mind, then analyze it again, thinking about it again, pondering about it again, recite it again, etc. Hence it is called a sotapanna (can also be translated as a wisdom enter from Ear)
Hope this help.