Salam Alaikum:
Does an adult child have to obey his / her parents in observing Islamic themes and fixing behavioral traits - in the case of: (a) child living with parents; and (b) child living separately from parents?:
1) Observing Islamic themes, such as cleanliness, discipline, organization, good appearance, avoiding allergic foods, taking care of health and fitness, utilizing time, being careful with expenditure, and not being lazy.
2) Fixing behavioral traits that negatively impact relationships such as being stubborn, argumentative, grudgy, controlling, arrogant, self-righteous, unable to understand situation or appreciate context, lack of consideration for others, using other people's belongings, unable to feel real remorse over past behavior, not feeling any empathy and not acting on empathy, not accepting mistake when pointed out. --------
What if the child feels that (s)he does observe Islamic themes and does not have negative behavioral traits? What if the child feels that (s)he is up to standard in these but the parents see otherwise?
Which standard should be followed: parents' or child's? Are there general guidelines for these standards, such as criteria of how the others evaluate a person or criteria from Quran and Sunnah?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, is His slave and Messenger.

Firstly, you surely know that parents are held in a high status in Islam and that Allah, The Exalted, joined their rights with His Right. He Says (what means): {And your Lord has decreed that you not worship except Him, and to parents, good treatment.} [Quran 17:23] He commanded children to show dutifulness and kindness towards their parents; He Says (what means): {Be grateful to Me and to your parents; to Me is the [final] destination.} [Quran 31:14] Therefore, a child should show dutifulness towards his parents to the best of his ability, especially given that parents are often compassionate towards their children and keen to serve their best interests.

Secondly, it is incumbent on you to comply (with your parents’ commands) with regard to matters that are obligatory under the Sharee‘ah, such as avoiding eating food that is harmful to the body, and matters that are prohibited under the Sharee‘ah, like the use of people’s property without their permission. The obligation of compliance in this regard is further emphasized by the parents’ command.

Thirdly, there is a general guideline that the scholars mentioned in this regard, namely that it is obligatory to obey the parents in what involves benefit to them and does not involve harm to their child, and we previously underlined this in Fataawa 131695 and 414148. The things you mentioned in the question involve benefit to you and, therefore, you have to obey your parents with regard to them.

The ruling on obedience to the parents is the same whether the child lives with them or lives separately from them.

Fourthly, the Sharee‘ah is the ultimate reference when it comes to determining whether or not a person’s conduct is good or bad. Actions should be judged according to the texts of the Quran and Sunnah, noting that the social customs are taken into consideration as long as they do not contravene the Sharee‘ah. It was reported that Ibn Mas‘ood, said: “What the Muslims consider to be good, is good in the Sight of Allah, and what they consider to be bad, is bad in the Sight of Allah.” [At-Tabaraani]

Allah Knows best.