Must one have intent to fulfill the mitzvah of honoring and fearing one’s parents when doing an act of honor or fear in order to fulfill the mitzvah?[1]

No. Since the mitzvah of honoring one’s parents is a mitzvah that is between man and his fellow, and the main aspect of it is what the parent receives, therefore, intent is not required in order to fulfill it. Furthermore, even if one explicitly has counter intent to not fulfill the mitzvah by doing a certain act of service for one’s parents, the mitzvah is still considered fulfilled.

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[1] Oneg Yom Tov O.C. 19; Sdei Chemed Mareches Mem Kelal 68; Likkutei Sichos 19:197, printed in Shuchan Menachem 4:173, based on Kiddushin 39b which brings the opinion of Rav Yaakov that there is no reward of a mitzvah in this world from the fact that a boy died in the process of climbing down the tree after getting the baby birds on behalf of his father. Now, if intent were to be required to fulfill this mitzvah then there would be no proof from this story as perhaps the son did not have intent to fulfill the mitzvah upon doing so, and hence he was not deserving of the reward of life. The fact that this option is not entertained by the Talmud shows that intent makes no difference in this matter and either way the mitzvah is considered fulfilled; See Sifri Ki Seitei 24:19 for a similar ruling regarding tzedakah the main thing is that the pauper received the charity irrelevant of what intent the giver had; See Malei Haroim Erech Mitzvos Tzerichos Kavana 9 regarding the mitzvah of circumcision that the mitzvah is fulfilled by physically doing the circumcision even if there wasn’t intent to fulfill the mitzvah; Likewise, see Minchas Chinuch Mitzvah 1 regarding the mitzvah of having children, that the mitzvah is fulfilled once one has a male and female child even if there was no intent to do so for the sake of the mitzvah