Ha Lachma Anya

Introduction

A Hodgepodge of Ideas?

After the breaking of the middle matzah at Yachatz, the Seder proceeds with the passage "Ha Lachma Anya".  This section is composed of three seemingly unconnected Aramaic sentences:

The first sentence of the passage speaks of the matzah eaten by our ancestors.  The next comprises an invitation to the hungry and needy to join in the meal, while the final statement expresses the hope for ultimate freedom and a return to the land of Israel.  What is the relationship between these three disparate themes?  Why were they combined into one section?

Additional Questions

• Placement – Why is Ha Lachma Anya sandwiched in between Yachatz and Maggid?
• Content – Though the opening sentence could relate to breaking the matzah, the continuation does not.  On the other hand, the passage also does not seem to be a direct retelling of the events of oppression or redemption.
• Pouring the Second Cup – While some Haggadot direct that the second cup be poured before the passage, others pour it after.  What does this tell us about the character of Ha Lachma Anya?.
• "הָא לַחְמָא עַנְיָא דִי אֲכָלוּ אַבְהָתָנָא בְּאַרְעָא דְמִצְרָיִם" – Although this sentence clearly speaks of the matzah eaten by our ancestors, it is not clear when it was eaten.  Does "לֶחֶם עֹנִי" refer to "poor man's bread" eaten while enslaved and afflicted, or to the matzah that was eaten at the time of the Exodus?  If the latter, why is it called "לֶחֶם עֹנִי"?
• "כָּל דִּכְפִין יֵיתֵי וְיֵיכֹל.. וְיִפְסַח" – It is strange that a person should be inviting someone to eat the Pesach offering, given that one is only allowed to participate in the sacrifice if counted beforehand (אין הפסח נאכל אלא למנוייו).  Moreover, the final line of the passage assumes that the speaker is not in Israel, in which case he would not be bringing the Pesach at all!  If so, what does "וְיִפְסַח" mean?
• Language – Why is this passage written in Aramaic, rather than in Hebrew as per the vast majority of the Haggadah?