couple of questions

There are a couple of locations where you can buy power armor and then there are places to find them one place to find it is at vault 106 in one of the lockers.
You can buy one at moira's crater side supply fro 35 caps.

1. Yes there should be an unlimited amount of puppies.
2. There's no real help anyone can give you if you're looking for Firelance. It is a random event that happens in a random spot anywhere in the game.
3. It is probably a Deathclaw because they run really fast and there is a glitch that makes them shoot up in the air.
4. I don't have any good spots, but I would try the Citadel.

1. I don't beleve that Dogmeat if dead can come back to live.
2. The Firelance randomly falls to the ground with the sounds of artillery
3. Either a Deathclaw Or a Gui Yao...
4. Theres a traveling caravan trader named 'Crow' he'll have some once you fully upgrade him.

1. Yup, if you have the puppies perk, he'll come back forever. His usefulness, however, is still next to nothing.
2. The Firelance is a random drop. When you're out walking about, an alien ship might streak across the sky. Search under where this happened (Have dogmeat help sniff it out) you'll find the Firelance and 24 alien power cells. Or you could just find the Alien Blaster, which is always in the same place when you go find it.
3. Probably a Deathclaw. Consider yourself lucky, because it's one of the toughest enemies in the game. Strong, fast, and really high HP. There's a very funny glitch that causes them to shoot up in the air, so it's most likely a Deathclaw. If you want to go see one up close, check Old Olney. It's in the Northeast corner of the map east of The Republic of Dave, and it's swarming with Deathclaws.
4. Pretty rare armor. I found a set in a locker in the Riley's Rangers compound, and if you upgrade Crow, he might have a set. Or, go through the story until you reach the quest, "Take it Back!", right after "The American Dream". Talk to Sarah Lyons in the Citadel before the beginning of the quest, and she'll offer you a spot on the Lyon's Pride, with it your choice of a set of Power Armor or Recon Armor. Then, tell her that you need a minute before starting the attack, and you can do whatever you want without starting the quest, which is also the end of the game, so that you can enjoy the Recon Armor.

Recon armor can be found in lockers in vaults
The firelance is found at random times listen for an explosion then look in the sky and if you see somting falling and look around on the ground for glowing tube which is the ammo and the gun should be near
If you want to see an encouter look on youtube

Firelance randomly falls from the sky I'm guessing you saw a deathclaw and theres recon armor at tenpenny tower