Summary:
All agree that מדרבנן a קטן can acquire a מציאה (through קנין יד), but not מדאורייתא. The dispute between ר"ל and ר"י is if a קטנה or a קטן can be קונה a מציאה, through קנין חצר.
These rulings are by a חצר המשתמרת , etc. - הני מילי בחצר המשתמרת
Summary:
In the case of משכונו של גר, if the משכון would have been in the רשות of the מלוה, he would have acquired it completely since חצירו המשתמרת is קונה שלא מדעתו, except by גט since it is בע"כ.
Perhaps it is a decree of the verse - דלמא גזירת הכתוב היא
Summary:
According to רש"י the question דלמא גזיה"כ היא is that we should change the גירסא of the ברייתא and therefore not be able to prove that עומד בצד שדהו is קונה. However תוספות rejects changing the גירסא and explains that the גמרא is merely trying to comprehend why the ברייתא could not have interpreted the פסוקים differently [and then there would be no proof].
The tithe which I will measure later - עישור שאני עתיד למוד
Summary:
רש"י maintains that ר"ג was actually separating מעשר to be מתקן the טבל in his house. תוספות maintains that ר"ג had already been קורא שם מעשר and (since it was זמן הביעור) was now distributing the מעשרות to their proper owners. [תרומה is separated in the field, while מעשר is separated in the house.]