If one already began one of these activities, what is the law?

Etz Yosef: If there will be time to pray Minchah after finishing, he may finish before praying.

Rav Elyashiv: Shevus Yakov (1:37) infers that once one began a Mitzvah, he does not interrupt, even to fulfill in a better way. E.g. if he was about to light candles for Ner Chanukah, and olive oil became available, he does not interrupt to light. I disagree. Here, once he began one of these activities, Chazal did not obligate him to interrupt if he will be able to pray later. It is not because he is considered to be engaged in the Mitzvah!

What is Ma'afores?

Rashi: It is a scarf. It is put on one who gets a haircut, lest hair fall on his garments. It is the first garment removed when undressing to bathe.

What is tying between his shoulders?

Rashi: He ties his sleeves.

What is the start of eating in Bavel and in Eretz Yisrael?

Rashi: Bnei Bavel girded themselves tightly; they untied the belt before eating. Bnei Eretz Yisrael did not do so before eating; for them, Netilas Yadayim starts the meal.

Tosfos: Even though R. Chanina was in Eretz Yisrael and Rav was in Bavel, we must say that R. Chanina addressed his Talmidim from Bavel, and Rav addressed his Talmidim from Eretz Yisrael.

Ha'Boneh: We learn from here that all enactments of Chachamim that depend on Midos, crafts or custom, they vary according to the people and the place.

Gilyon ha'Shas: Bnei Bavel are called "Chagurei Azor b'Masneihem" (Yechezkel 23:15).

If he already washed his hands, why may he eat before praying? If one must wash before praying, we can consider that he washed for Tefilah! There is no extra exertion, for in any case he will need to wash for Tefilah!

Daf Al ha'Daf: Over Orach (233) left this difficult. He can guard his hands during Tefilah, and not need to wash again to eat!

Rav Elyashiv: We may infer from here that there is no need to wash for Tefilah. (NOTE: Shulchan Aruch (OC 233:2) says that if one has water, he must wash for Minchah. Bi'ur Halachah brings from Magen Avraham that if one washed to eat and wants to pray, he must wash again. i.e. one must wash with intent for Tefilah! However, the Magen Avraham said if one washed to eat and ate and wants to pray, he must wash again. This implies that if he did not eat, he need not wash again. Below (10a) Rav Elyashiv suggested that perhaps one must wash for the sake of Tefilah. - PF.)