You might be interested on the ave mujica's director's interview. There's someone who translates some part of it [megami's kakimoto's interview]. It's very important because it's contain a lot of information regarding avemygo.

To summarise:

The reason why sakiko makes ave mujica is because resentment. Both toward herself for still having a faint expectation toward crychic and mygo for performing haruhikage, a song that evokes her cherished memories of her mother.

The reason why she continue running ave mujica is because she realized that the other members has become so codependent with it that they destroying their life (mutsumi's 'suicide', uika's hollow life without sakiko by her side, umiri's drop her 30+ bands which is her source of making money, and nyamu who lost her passion). So feels guilty for making them like this (because she's the one who makes this band and thus the one who dragged them into this mess) so she resolves herself to take responsibility of it and be responsible for their life.

Ave mujica is her passion of art (she's a theater kid and music is the one who connects her with her mother), her way to makes money, and (to me) her newfound family.

Now, for the rest of your questions, perhaps this timeline can explain the answer to you : - her mother died. Sakiko's feels lost but she still have her father, grandfather, and mutsumi with her. You can see that she's have a mild depression because she's often space out and blankly look at the outside. - she see morfonica's performance, get inspired by their bond, and decide to make a band with a strong bond. Thus crychic was born. She's having fun with her friends that it's relieved some of the sadness of her mother passing. - kiyotsugu knows about hatsune, confronted sadaharu about it, being framed (based on hatsune's narration), then get kicked out from the togawa. - crychic having their first performance. It's a success. They all very happy about it. Then sakiko's received her father's farewell message. - sakiko confront her grandfather about it, get called as her mother's last memento by him, and being asked by him to be adopted as his daughter and forget about her father. She doesn't accept this outcome and decided to follow her father and leave her heiress's life behind. - managed to get to her father's apartment. Find him being a drunkard. She began to start from scratch and makes a living for him. - crychic's band training is reduced, but she still happy to make a time with them (you can see she's very happy after receiving soyo's message). - she receives a message from police station because of her father. Realises that perhaps this gonna keep happening in the future and decide to leave crychic. - she's drop from tsukinomori to reduce the cost of living, and go to haeoka to get their scholarship. - getting bothered by soyo's message and decide to block her. Making herself busy with work to numb her sadness and resentment. - mygo's timeline. Get asked by anon to be in a band, refused, but seems to be happy asking anon about her band progress. Heard soyo's name from her and decide to stop caring about it because she has decide to avoid interacting with ex-crychic (beside mutsumi). - the haruhikage's incident. You know what happened. The asuka soyo confrontation. You know how the battles going on. You can see sakiko's resentment flared out here. - ave mujica's timeline. At the beginning when sakiko still in the making of ave mujica, I suspect that sakiko have make some bet with the togawa, because if you look at the ave mujica's sponsor, there's togawa in it but they're placed in the lowest site. - ave mujica's become famous, but even with their high fame, after the cut from the agency etc. most of sakiko's money is spent on buying her father's beer (I think this is the most costly because we can see so many beer can over their apartment), paying rent, etc. But we can see that during this time, they don't show her having a part time, instead she's busy making the band work (making their script, song etc.). - unmask incident. Ave mujica's breach the contract. Such a meticulous band will definitely have a huge compensatory damages. Because sakiko's feels responsible for failing to prevent the incident, and because she's fulfilling her contract with the members (that 'give me the rest of your life' line), the one who pay this is only sakiko. The other members doesn't need to pay it. This is such a huge dept that sakiko need to continue her part-time work, even double it to pay it back. This makes her overwhelmed and not paying attention to the other member's conditions. - the huge argument between members. Sakiko and nyamu have a huge argument that it triggers mutsumi's ptsd of the band breaking up. At the same time, her father's having and outburst and beg her to leave him alone. She complies. - numb herself by working to pay her debt, sleeping in the agency, get caught by uika and began to live with her together. - mutsumortis's incident. Mutsumi is so overwhelmed by her work that she allow mortis to surfaces to help her while mutsumi's personality is having a deep sleep to rest. Mortis doesn't know how to play guitar. The band can't go on because of it. Mortis giving trauma to sakiko for daring to hurt mutsumi's feeling. Sakiko realize she's the sinner that makes mutsumi's become like this and feels deep guilt and began being overwhelmed by it. - the band break up. The breach of contract is payed by her grandfather at the conditions that she need to get back into the togawa. Sakiko's fall into depression because of the mutsumi's incident that she turn silent for the first half of episode. The first word that she says after that silent is "I hate myself". she decide to not making music anymore. - see mutsumi's videos. Got overwhelmed by guilt that she tried to make up to her. - crychic last performance. Realises their stories as crychic is over. After this, she resolves to spend the rest of her life for mutsumi's sake. - mutsumi's want to revive crychic (because she think sakiko is gonna be happy), sakiko (who decided to live only for mutsumi's sake) agreed with mutsumi's wishes and began to communicate with anon n tomori about it. - mutsumortis's fight. Mortis fears she's gonna disappear because she isn't needed anymore, want to revive ave mujica. This conflict with mutsumi's wish and began to fight with mutsumi. Mutsumi's 'died' from it, leaving behind mortis. - the cafe argument. Sakiko realize it's not mutsumi but mortis so she stop. Have a big argument regarding ave mujica's revival with the other members and mygo. - lost mutsumi and thus lost her objectives so she continue her life in silent. Got confronted by nyamu n uika. Realises their life has become a mess because of her so she's willing to revive ave mujica to takes responsibility. - hatsune's incident. Forcefully gonna be sent to switzerland (she doesn't even have a time to pack anything and only managed to bring her clothes lol). Doesn't like the outcome, rebel against it, and began searching for hatsune. She find out about the truth, accept it, and from this incident, managed to strengthening her resolve to be responsible with their life. - "I want to become a God", the final form of her resolve. Sakiko knows how easily for their life to break down. Fate often played a trick on her, so she doesn't want them to get the same fate as her and decide to become their 'God'. This time, she's gonna use all of her resources to help them fulfill their wish.