WHERE THE CUSTOM OBTAINS TO REPEAT [THE VERSES OF HALLEL],
HE SHOULD REPEAT; [WHERE THE CUSTOM IS] TO SAY THEM ONLY ONCE, HE SHOULD SAY THEM ONCE;
WHERE THE CUSTOM OBTAINS TO REPEAT. It was taught, Rabbi used to repeat [certain] words in it [From אנא השם and on - Rashi];
R. Eleazar b. Perata used to augment [certain] words in it. What is meant by ‘augment’? — Abaye explained, He augmented the doubling beginning with אודך ‘I will give thanks unto You’
to the end of the Psalm.
[WHERE THE CUSTOM OBTAINS] TO RECITE THE BENEDICTION, HE SHOULD
RECITE THE BENEDICTION. Abaye explained, This [that whether you make a bracha on hallel is dependent on minhag] was taught only with regard to the concluding benediction,
but with regard to the preceding benediction, it is a positive commandment to say it, for Rab Judah citing Samuel ruled, With all commandments the benediction is to be recited ‘over' [prior] to their performance [עובר לעשייתן]. And whence do we know that the word ‘over' means prior? — R. Nahman b. Isaac replied, Since it is written, Then Ahimaaz ran by the way of
the plain and he overran [קדמו לרוץ לפניו preceded him - Rashi] the Cushite.
In the parallel sugya [Psachim 119 - see there] the gemara says about hallel on the arba kosos that if the custom is to repeat - he should repeat. Rashi there explains the "repeat" refers to the entire hallel. That is a blatant contradiction to what Rashi says here that the most one repeats is from אודך but not the whole hallel. Rashi [in the mishna ד"ה לכפול] explains that the reason there is a custom to repeat is because most of the mizmor of הודו לשם is composed of repeated psukim so we have a custom to repeat them all. But there is no reason to repeat the psukim of the rest of hallel that is composed of other mizmorim that aren't repeated. So how can we reconcile the contradiction between Rashi in Succah with Rashi in Psachim?
There is another contradiction betwen the two parallel sugyos. The gemara in succah first discusses the repetition of psukim and then gets to the bracha on hallel which is the order of the mishna. The gemara in Psachim switches the order and first discusses the bracha and only then the doubling of psukim contrary to the order of the mishna.
Let's see another parallel gemara [Psachim 7a-b]: Rav Yehuda said that one who searches for chametz must make a bracha beforehand of על ביעור חמץ. The gemara explains: Because Rab Judah said in Samuel's name: For all precepts a benediction is recited prior [‘over'] to their being performed — Where is it implied that this [word] ‘over' connotes priority? — Said R. Nahman b. Isaac, Because the pasuk said, Then Ahimaatz ran by the way of the Plain and overran [ויעבור] the Cushite. Rashi explains - קדמו במיתת אבשלום - Achimaatz preceded the Cushite in reaching Dovid to relate the death of Avshalom.
This is a huge problem. If you look in the psukim [שמואל ב' פרק יח] you will see that Achimaatz did not outrun the Cushite to relate the death of Avshalom but to tell Dovid that they were victorious in battle. Only after he told Dovid about the battle Dovid asked him how Avshalom was and he replied that he didn't know. So why is Rashi not following the simple understanding of the psukim?
Huge problem.
We learn from the Rashi in Psachim a new understanding of the whole story of Achimaatz who asked Yoav permission to tell Dovid the news and Yoav answered that it's not good news so he shouldn't go. Ahimaatz said that he wants to go anyway. When he arrived he said "Blessed is Hashem who delivered into our hands the men who raised their hands against my master the king" [כ"ח]. When Dovid asked about Avshalom, Achimaatz answered "I saw the great commotion when Yoav sent the Cushite servant of the king etc. and I do not know what happened".
The meforshim explain that Yoav didn't know that Achimaatz would only tell Dovid about the victory at war and wouldn't tell him about the death of Avshalom. The Malbim adds that the whole idea to tell only part of the story [the victory and not the death of Avshalom] came about only after the Cushite was sent to tell Dovid the bad news. Since there is already a messanger to relate the bad news he is free to share the good news only.
HOWEVER, from Rashi in Psachim we learn a new understanding of what happened. Achimaatz intended to tell Dovid the whole story because the shleimus of being a good messanger of Yoav is telling the whole story. The chochma of Achimaatz was that he was able to veil the news in very vague terms, so he told Dovid and didn't tell him at the same time. When he said "Blessed is Hashem who delivered into our hands the men who raised their hands against my master the king" he was alluding to Avshalom as well. When Dovid asked him specifically about Avshalom he gave an evasive answer "לא ידעתי מה" - I don't know what happened afterwards [Rashi on the pasuk there]. That didn't answer Dovid's question at all because he didn't want to be explicit about Avshalom's death in order to leave Dovid with some hope.
But now we are left with the question of what compelled Rashi in Psachim to understand the parsha that way.
We can make the following chakirah: Is the bracha before a mitzva a declaration of intent that the act is being done for mitzva purposes [there is a Ritva somewhere who says that] or do we say that the bracha is part and parcel of the mitzva and not just a hakdama. Rashi clearly holds like the second side of the chakira - that the bracha is part and parcel of the mitzvas bedika. Rashi doesn't hold like those poskim who say that the bracha is made on the bedika because the bedika is the beginning of the biyur but that the bedika is significant enough to warrant its own bracha as he writes ולשון ביעור [בברכה] היינו נמי בדיקה. The bracha is on the bedika and is part and parcel of the bedika.
This explains why in Psachim Rashi understood the psukim as he did. When Achimaatz outran the Cushite it was to perform the very same shlichus that the Cushite was performing, namely to relate the death of Avshalom. This parallels the issue at hand, the statement of Rav Yehuda the bracha precedes the mitzva and where according to Rashi they are the same entity.
In contrast to this, in our sugya Rashi explained the Achimaatz קדמו לרוץ לפניו - He outran the Cushite to tell him something different [not מוכרח but could be]. This is consistent with the first way of understanding the bracha on the mitzva - that it is a declaration of intent that a mitzva is to be performed [and thank Hashem for the honor] but a different entity from the mitzva.
I didn't answer all the questions but if you look at the sefer Marbeh Yeshiva [סימן ח] from Rabbi Homnick Shlita everything will become clear.
