Where in Egypt Did the Israelites Live?

Introduction

In Goshen or Beyond?

Upon their arrival in Egypt, Yosef settled his family in the land of Goshen, and the Torah notes that they struck roots and prospered there:

EN/HEע/E
(בראשית מז:כז) וַיֵּשֶׁב יִשְׂרָאֵל בְּאֶרֶץ מִצְרַיִם בְּאֶרֶץ גֹּשֶׁן וַיֵּאָחֲזוּ בָהּ וַיִּפְרוּ וַיִּרְבּוּ מְאֹד. 
(Bereshit 47:27)  And Israel dwelt in the land of Egypt, in the land of Goshen; and they got them possessions therein, and were fruitful, and multiplied exceedingly.

It is unclear, though, if the nation remained exclusively in Goshen, or if at some point they spread beyond its borders into greater Egypt.  Shemot 1:7 describes the nation's proliferation:

EN/HEע/E
 וּבְנֵי יִשְׂרָאֵל פָּרוּ וַיִּשְׁרְצוּ וַיִּרְבּוּ וַיַּעַצְמוּ בִּמְאֹד מְאֹד וַתִּמָּלֵא הָאָרֶץ אֹתָם.
And the children of Israel were fruitful, and increased abundantly, and multiplied, and waxed exceeding mighty; and the land was filled with them.

The phrase "וַתִּמָּלֵא הָאָרֶץ אֹתָם" is ambiguous; does it suggest that as the Israelites multiplied, they left their original settlement and permeated the Land of Egypt as a whole, or does it mean more simply that they filled only the region of Goshen?

Isolation or Integration?

A second question relates to the level of interaction between Egyptians and Israelites.  Were the two nations segregated from each other or did they live as neighbors?  On the one hand, regarding the plagues of arov and hail,  the text mentions a geographic distinction between Goshen and Egypt proper ("וְהִפְלֵיתִי בַיּוֹם הַהוּא אֶת אֶרֶץ גֹּשֶׁן"), suggesting that Israelites lived in one and Egyptians in the other.  Moreover, in explaining the impetus to move to Goshen, Yosef asserts that shepherds were an abomination to the Egyptians ("כִּי תוֹעֲבַת מִצְרַיִם כׇּל רֹעֵה צֹאן"), again hinting that the Egyptians preferred to maintain their distance from Yaakov's family.

On the other hand, the commandment to borrow vessels from one's neighbors and tenants ("וְשָׁאֲלָה אִשָּׁה מִשְּׁכֶנְתָּהּ וּמִגָּרַת בֵּיתָהּ") presumes that Egyptians lived close to, and even in the same homes as the Israelites!  Similarly, the smearing of blood and skipping over homes ("וּפָסַח י"י עַל הַפֶּתַח") during the Plague of Firstborn implies that the houses of the two peoples were in close proximity.

Implications

The above questions have implications for a variety of other issues.  These include:

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