Thank you for your questions.
1) Hadith are distinguished as trustworthy or not using a number of methods explained in the science of hadith. There are hadith that are acceptable in books by Shia authors and there are hadith that are not acceptable in those books. In the same way, there are hadith that are acceptable to Shias in books written by Sunni authors and hadith that are not acceptable. But distinguishing these hadith is the work of a scholar and so instead of not relying on any hadith on any subject it is perhaps wiser to refer to a learned scholar on which hadith can be accepted and which are not authentic. It is also important to understand the purport and the context of different hadith and that perspective can also be given by someone who is qualified to do so.
2) According to the school of Ahl al-Bayt (as) there is no confusion over the successor of the Prophet (saw) being Ali b Abi Talib (as) and the proof of this claim is found in our reading of the scriptural sources as well as what has been narrated by all denominations of Muslims. These proofs are detailed in the appropriate works.
3) The hadith which mention parts of the Quran being lost narrated from Aisha (if we are to accept them as authentic) are referring to her copy of the Quran, not to the Quran of the Prophet (saw) which was in the possession of Imam Ali (as). Muslims of all denominations are agreed that there has been no addition or subtraction from the text of the Quran and again the proofs for this are numerous and are found in books of the science of the Quran. As for Shia narrations concerning subtraction from the Quran, the meaning of these traditions returns to a forgotten meaning of those verses rather than an actual subtraction from the text of the Quran.
4) I am not aware of the specific narration you are referring to but Sunnis and Shias are agreed in the number of prayers being 5. The difference is that Shias can join the Zuhr and Asr prayers after the time of Zuhr (as the specific time for Zuhr is the amount of time it takes to pray the Zuhr prayer) and likewise the Magrib and Isha prayers, without a specific reason. This is because we have narrations explaining that the Prophet (saw) joined these prayers without a specific reason. But Shias are also at liberty to separate these prayers too as long as they are prayed within their appointed times. So it is possible to pray Zuhr after the sun passes the midpoint of the sky and to pray Asr in the late afternoon, for example. At the same time, it is acknowledged that the Prophet (saw) would usually separate the prayers. At any rate, there is no doubt that there are 5 daily prayers.
5) During the caliphate of Imam Ali (as), Aisha, Talha and Zubayr lead an uprising against Imam Ali (as) in a battle called the battle of the Camel. It was named this because Aisha mounted a specific type of camel on the battlefield. The event is undisputed and is a historical fact.
6) Aisha is respected amongst all Muslims as the wife of the Prophet (saw), however in the light of certain positions she took during the life of the Prophet (saw) and after his (saw) death, most Shia scholars do not consider her a reliable narrator of hadith.
May you always be successful.