It is preferable to complete the soorah that you have started, but if you move to another soorah before completing the first one, there is nothing wrong with that and your prayer is valid.
Raising the hands during the prayer is one of the Sunnahs of the prayer. So if you raise your hands, it is Sunnah and is not a mistake, as you thought. But if you do not raise them, that does not affect your prayer. The same applies to putting them on the chest after rising from bowing. Please see the answer to question no. 3267 for information on the points when the hands should be raised.
With regard to the manner of sitting, please see the answer to question no. 103886. For a description of the prayer of the Prophet (blessings and peace of Allah be upon him), please see question no. 13340.
As-salaah al-Ibraaheemiyyah [durood] is Sunnah, so if you omit a letter or two, you do not have to do anything and your prayer is still valid, in sha Allah.
If the mistake occurs in al-Faatihah, then it must be corrected, because al-Faatihah is a pillar or essential part of the prayer, without which the prayer is not valid. But if the mistake is other than in the recitation of al-Faatihah, it must also be corrected, but it does not invalidate the prayer, even if you do not correct your recitation whilst you are praying. Similarly, there is no blame on you if you move from one soorah to another, even though it is preferable to complete the soorah which you started. And there is nothing wrong with you repeating the same soorah after al-Faatihah in every rak‘ah, or in every prayer, if that is easier for you or if you have memorized it better than others.
The Sunnah in prayer is for the worshipper to look at the spot of prostration. Please see the answer to question no. 25848. And it is makrooh (disliked) to look around whilst praying. For a detailed discussion on that, please see the answer to question no. 160647.
If your prayer is invalidated in some way, that does not necessarily mean that your fasting is invalid, because there is no connection between the two.
It is obligatory to cover the ‘awrah whilst praying. If a woman prays with her ‘awrah uncovered, her prayer is not valid. The woman’s whole body is ‘awrah during prayer, apart from the face and the hands, so she must cover all of her body. For more information, please see the answers to questions no. 135372 and 126265
If the nature of the garment you wear is such that every time you bow or prostrate any part of your body becomes uncovered (the neck, chest or anything else), then prayers offered when wearing it are invalid, because of what is mentioned above about it being obligatory to cover the ‘awrah
An-Nawawi (may Allah have mercy on him) said: If a person prays in a chemise with a wide opening in front and his ‘awrah can be seen from above when bowing or prostrating or at other points in the prayer, his prayer is not valid and he should fasten that opening, or tie something around his middle, or put something over the opening that fastens on his shoulders, or the like…
End quote from Rawdat at-Taalibeen (1/284)
But if the uncovering is accidental, such as if the garment rides up without him intending it to, and some part of the ‘awrah becomes uncovered, then what the worshipper must do is hasten to cover up whatever of his ‘awrah has become uncovered as soon as he realizes that that has happened. His prayer is not invalidated by that, and he does not have to repeat it.
See also the answer to question no. 135372
With regard to the prayers that you offered before that in which there were some mistakes, there is no blame on you for whatever you did when you were unaware of the rulings, and you do not have to make up any of them. Rather you have to try hard to learn and find out what is correct from the Sunnah from now on, but without getting carried away by insistent thoughts or becoming paranoid, so that the Shaytaan will not spoil your worship.
And Allah knows best.