Why did the brothers see fit to inform Pharaoh that they had only come to sojourn, because there was no pasture for their animals... ?
Ramban #1 1 : Presumably in Kena'an, where there was no grain to be had, the people ate whatever they found growing in the fields, leaving nothing for the animals. This was not the case in Egypt, where grain was available, leaving the little that grew for the animals.
Ramban #2: It is even possible that due to the many canals and pools, there were areas in Egypt where pasture was available for the animals.
Rashbam: To disillusion him from the assumption that they had come to take advantage of Yosef's position.
The Ramban actually comes to answer the question that, due to the famine, which was perhaps even more intense in Egypt, there was no pasture for the animals there either?
Why did they say, "la'Gur ba'Aretz Banu," rather than 'la'Sheves... '?
Rashi: Yaakov went down to Egypt only to sojourn, and not to settle down permanently. 1
The Ba'al Hagadah praises Yaakov for that, implying that it was on that merit that his children were eventually able to leave. See Bereishis 15:13. Refer also to 47:27:1:2.
Mizrachi asks - Did the brothers request the entire land of Goshen? Wasn't this much more than they needed?
Gur Aryeh (to 47:11): Their main request was to live in [some part of] the Land of Goshen -- rather than in Egypt proper.