Why can't residents of a city testify about a communal Torah scroll that was stolen?
A Torah scroll is made to be heard by all — no one can withdraw their share of 'interest' in it. Therefore none of the city's residents can testify or judge in the matter.
Question 2
What must a business partner do before he can testify on behalf of his co-partner about shared property?
The partner must perform a formal kinyan transferring his share to the co-partner and committing to reimburse him if a creditor expropriates the property. Only then may he testify.
Question 3
Can a sharecropper testify on behalf of the field owner if the field currently has produce in it?
The sharecropper wants the owner to retain the field so he can receive his portion of the produce. This financial interest disqualifies him. If there is no produce, he has no stake and can testify.
Question 4
Reuven guaranteed Shimon's debt and Yehudah claims Shimon's property. When can Reuven testify that the property belongs to Shimon?
If Shimon has another field to cover the debt, Reuven the guarantor has no stake in this particular field — the creditor can collect from the other field. Therefore he is not a 'nogea b'eduto' and may testify.
Question 5
What general principle does the Rambam state about when a witness with a conflict of interest cannot testify?
Rambam writes that even if a witness derives benefit in a 'remote and wondrous way' (derech rechokah v'nifla'ah), he should not testify. The judge must be deeply perceptive to uncover even indirect interests.