How do the elements of the story tie together? (SPOILERS OBVIOUSLY)

4. How is Madeleine the love interest of the world's greatest spy, AND the doctor of the world's biggest terrorist, both of whom also happen to be brothers?

It doesn't make much sense if you bother to think about it. If the US wanted to capture someone in a foreign country like Cuba they would either say fuck it and just send in a special ops team or if they were trying to be covert would hire someone to do it but if they hired someone it would have been locals to avoid it coming back to them if it failed... they would not hire a british person to do it. I mean they had the latino woman in Cuba already and she was pretty much as effective as Bond so why in the fuck would they have hired someone that would stick out like a sore thumb to try and kidnap a person in Cuba... It was a major plot hole.

As for why Safin kidnapped them, they didn't provide any reasonable explanation, nor did they bother to explain why Safin needed nanobots that only killed specific people, notice when bond looks at the way the deaths are supposed to happen and the fact that when a worker falls in the pool of nanobot thick water they die... and the whole world's population was supposed to die... Why the fuck would you bother with nanobots? All you needed to do was use massive amount of poison or unleash a virus on the world you don't need to go to the trouble of trying to get special nanobots that would then have to be reprogrammed to kill everyone. It made no sense. Nor did telling bond he was now infected and his touch would kill the woman and kid, hell the woman and kid were already going to die based on the nanobots being set to kill everyone so why even bother to throw in a special nanobot just for the girls. It was another device that was thrown in just to explain why Bond was going to kill himself... In the end this was one of those movies that required you to watch it without thinking because if you thought about it there were so many stupid things that you would just shake your head in disgust.

because good writing is now a wasted talent

Actually adding to the above I'm seen all of James Bond films, and there has not been one film where I actually fully understood the plot.

My replies are completely serious.

1. Why did Leiter (and later Nomi) even approach 007 in the first place?

Because he's Bond. James Bond.

2. Why did Safin kidnap Madeleine and Matilde?

Because he's EEEVILLLLL. That's what eeevilllll masterminds do.

3. Why should Safin have a grudge against Bond? If anything they should be allies. They both want to take down Blofeld and Spectre?

He shouldn't.

This was the emptiest, laziest plot for a Bond movie that I've seen in a while.

3. Safin wanted rid of Blofeld and Spectre because of his personal grudge but he also had his own ambitions for world domination. He recognised that Bond was the most kick ass person on the planet and would be a serious threat to him.