Favortism is not allowed to be shown regarding collecting from Peah. However as the Posuk indicates Boaz was allowing her to collect even from his own personal stuff גַּם בֵּין הָעֳמָרִים תְּלַקֵּט which there it belonged to Boaz and he is allowed to do whatever he wants.
Mishna Peah Chapter 1, Mishna 4:
כלל אמרו בפאה. כל שהוא אוכל, ונשמר, וגידוליו מן הארץ, ולקיטתו כאחת, ומכניסו לקיום, חייב בפאה. והתבואה והקטניות (1) בכלל הזה.
First principle, fruits that must met five criteria.
Food, => not plants for the production of dyes,
In a guarded place, => not wild plants,
Grows on the ground, => not mushrooms and ...
Peah has to be designated by the owner. It also doesn't have to be in the corner of the field, but it does have to be at the end of the owner's harvest. (Peah 1:3)
Also, even if it is designated, you can only take it if you're poor (this is in the pesukim you quoted, Peah 8:8 gives the criteria to be poor).
Peah also only applies to a few kinds of trees (...
This excellent question is asked by the Gemara in Chulin 134a(¹), you can found it learning the Mishnayot chulin 10, 4 in TYT and Tif'eret Yisrael.
The conclusion of Rava is that:
Kama beChezkat chiuva, when last sfekot which are ruled as Hamotsi mechavero alav hareaya are cases of Chezkat ptur.
פרה. כשנולד לך ספק זה במתנותיה ואתה ...
The source is in Kiddushin 40a:
"מחשבה טובה מצרפה למעשה, שנאמר: אז נדברו יראי ה' איש אל רעהו ויקשב ה' וישמע ויכתב ספר זכרון לפניו ליראי ה' ולחושבי שמו, מאי ולחושבי שמו? אמר רב אסי: אפילו חשב אדם לעשות מצוה, ונאנס ולא עשאה, מעלה עליו הכתוב כאילו עשאה.
The Gemara further teaches: The Holy One, Blessed be He, links a good thought to an action, as it is ...
"Kol Hamarbeh Lisapir Byitziyas MitzRayim Haray Zeh Mishoebach" means that when extending the time past the end of the zman, one is to be praised even though one is no longer fulfilling the mitzvah. Note that the story has Rabbi Elazar ben Azaryah continuing to speak of Yetzias Mitzraim past chatzos even though he held that the seder had to end at chatzos. ...