Hm. Thread got long before I saw it. Where to begin...
On Vampire-fu: That one quote about taking martial arts before dying aside - vampires are a demon in a human body. Is it so odd to thing that in general these demons know how to fight?
Why didn't Buffy just kill off the original threatening vampires and go and live her life? Because she's not an idiot. She is in Sunnydale, and has to live there. Exactly what has she to gain from ignoring the problem?
Why doesn't Buffy demand conditions favorable to her? Probably because the people she was dealing with weren't in a position to grant such conditions. Giles works at the school, but doesn't ahve the administration under his thumb. He cannot grant good grades and remove homework.
Why didn't the authorities do something? Well, the Mayor was a big part of that, as we find out later.
Why is the Watcher's Council a bunch of idiots? Because, at any given time, there's only one Slayer. The way they've set it up, that means that at any given time, there's not many of them that have real field training. You need many Watchers to cover all the potentials, but most of them live boring lives watching a teenager grow up.
Why don't Buffy and Giles sit down and talk? Dude, you're talking about a world in which marriages fall apart due to lack of communication. Actually talking about things is not a human strong suit...
Why don't vampires use weapons? Because they are weapons themselves. That goes both for vampire psychology, and for dramatic necessity. More primitive battle is generally more appealing to viewers. And really, you're talking about a demon. It may not be dumb, but it automatically thinks that it is physically superior to any human. It is only rarely when they would need weapons.
Why don't the vampires go after Buffy's family and friends? Because that's not terribly constructive. What's more effective - killing the Slayer, or giving her a real personal reason to put a stake in your heart?
About evicting Buffy in the final season -
Edena, you talk about Buffy, Faith, and Spike as weapons. But that treats them as mechanisms, and they aren't merely mechanisms. They are people, and so the situation was far more complicated.
Or, to follow your analogy - the weapon is useless if the arm and mind that wield it are tired or foolish. Eviction was not irrational. It was, in fact, exactly what Buffy needed at the time. SHe was near teh breaking point, and needed perspective and time to think forced upon her, as she would not take it willingly.