1- No. Except if they asked to buy them from their 1/3rd, or they asked to do so without pointing to the 1/3rd.
In both cases, if the cost was higher than 1/3rd of what they left, the balance is to be either paid by the eldest son for the father's prayers and fasts, or he should perform them personally.
For the mother, it could be shared by all the offspring, if they agreed.
2- Already answered in 1.
3- Only for the father, and recommended for the mother.
4- Yes.
5- If they were capable to do hajj, but they did not, then, it is to be extracted from the inheritance before distribution, while if the offspring decided to perform a recommended haj for him/her, even because he/ she was not capable to go to hajj for any legitimate reason, then, the cost is to be deducted from the shares of those decided to do so.
6- Already got clear from previous answers.