plagues makkos - What is considered to be "firstborn"?

This is probably a bit pedantic and beside-the-point, but here goes: in Exodus 12 (I am reading the Jewish Publication Society translation), we have:

12 For I will go through the land of Egypt in that night, and will smite all the first-born in the land of Egypt, both man and beast; and against all the gods of Egypt I will execute judgments: I am the LORD. 13 And the blood shall be to you for a token upon the houses where ye are; and when I see the blood, I will pass over you, and there shall no plague be upon you to destroy you, when I smite the land of Egypt.

Later:

29 And it came to pass at midnight, that the LORD smote all the firstborn in the land of Egypt, from the first-born of Pharaoh that sat on his throne unto the first-born of the captive that was in the dungeon; and all the first-born of cattle. 30 And Pharaoh rose up in the night, he, and all his servants, and all the Egyptians; and there was a great cry in Egypt; for there was not a house where there was not one dead.

I was wondering about what is meant to be considered "the firstborn" in this context, beyond possibly referring to male children - this detail is something I'm not sure of, since I have absolutely no idea where I picked it up. (My guess - from reading Wikipedia - is that this should be correct.) Moreover, from the second passage, this would suggest that this applies to the firstborn of each intra-family generation to me. However:

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  I'm merely making an educated guess here. Am I correct on the above points? It strikes me as slightly weird for, for instance, a firstborn elderly man to die, but this is something that I can "live" with.

  
  
  


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  Is there any indication (whether textual, or through some sort of tradition) if this applies to the firstborn of a father, or to that of a mother? Naturally in many cases, this shouldn't matter, but in others (e.g. remarriage of widowed individuals) it does.

  
  

These aren't really issues that affect the meaning of the text for me, from a "moral" angle, but I'm curious about whether or not some specifics are ever actually addressed.