Passover - the Passover-lamb that our fathers ate during the time of the Beis Hamikdash - for what reason did they do so?
Because the Omnipresent passed over our fathers' houses in Egypt, as it is said: "You shall say, It is a Passover-offering to the L-rd, because He passed over the houses of the children of Israel in Egypt when He struck the Egyptians with a plague, and He saved our houses. And the people bowed and prostrated themselves." (From the Passover Haggadah)

G-d needed to instruct the Jewish people to place the blood of the Pesach sacrifice on their door post's in order that they should be saved. Why was the plague of the first born also directed at Israel?

Also, why is the concept of "pass-over" only associated with the plague of the first born? Hashem also passed over the Jewish on the other nine plagues.

The Maharal of Prague explained that the Egyptians believed that materialism was the ultimate reality and spirituality only developed as a result of it. The first born represented the strength of humanity and thus the height of spirituality.

Hashem want to show the Egyptians that true spirituality is not an extension of man's "development" but rather the ultimate reality which can only be reached by having a direct relationship to Him. By also directing the plague towards the Jewish people and causing our salvation through the fulfillment of His commandment the Egyptians saw our connection to the Creator.

The Torah is not a philosophy or some nice ideas. The Torah is our direct relationship to the Master of the Universe who ultimately controls everything. Passover is the time to reconnect to Hashem with the understanding that nothing is beyond His power. We can totally transform our lives if we decide to serve Him in truth.

How about Nissan 6th?

Please clarify.