I am wondering if there was really a poisoning at all.. Londons behaviour lately regarding not allowing entrance to people to the UK who have voiced openly Non-Mainstream opinions (like Lauren Southern) does not shed a good light on this country in any way. It seems like there is a strategy at work to worsen relations between NATO and Russia in order to prepare the playground for a military aggression.

No Evidence and No Independent Examination

Russia wanted to get access to the victims in order to examine for themselves, but access was not granted to anyone as far as I know. The possibility therefor exists that there was no poisoning at all in the first place. Everybody says that it is very likely that it were the Russians, but no hardcore evidence was provided. The only motive they say is that Russia wanted to punish ex-traitors in order to set an example. (Even though that they now did not post any risk at all from an intelligence-viewpoint).

Based on no evidence all of the NATO-countries expelled russian diplomats

It is really a shame, that without having a shred of evidence so many (27) countries expelled diplomats. But really, the culmination was condemning the counter-measures by the russian government, as the US did...
First they should bring solid evidence to the table and afterwards talk about sanctions and expelling diplomats. Not without.

Why would Putin do it a few days before his reelection??

I think this is something that really should one make this doubt... If Putin wanted him killed, I am quite sure that he and his advisers would be intelligent enough to do it after his reelection 5 days later.

Why does NATO want war with Russia

Russia is one of the very few independent countries left on the planet, which counts.
The easiest way to capture a country is to switch their leaders to someone who in reality works for foreign interests. In Russia it has failed again and again... So in the end they might not see another way than to attack the country. But you have to sell the idea that they are just spreading democracy and freeing the people there... That good deeds are been done...

Needless to say that NATO does not care about the millions of deaths that could follow a military attack, but for now technology-wise the Russians seem to be ahead with their Sarmat (nick-named by NATO Satan-2) missile, which allegedly cannot be stopped by missile defenses... This disadvantage really stops NATO in my eyes from going ahead and entering war with Russia.
https://edition.cnn.com/2018/03/30/europe/russia-missile-test-sarmat-intl/index.html