Plutonium & Nuclear weapons

How do i make plutonium for nukes?

Nuclear fuel from a reactor can be processed in a plutonium processor once it reaches 50% of its life remaining, the amount of plutonium that processing creates depends on the life of the fuel and the type of reactor it was used in, fully spent fuel with 0 life remaining produces the most plutonium, so you can choose to either process it early or wait until its fully spent to get the maximum amount which can take up to 2 years.

The type A reactors only have a plutonium conversion ratio of 0.6 or 60% and the advanced reactors have a ratio of 1.2 or 120%, the conversion ratio is a measure of how much MOX fuel you can create from the processed plutonium, so 1.2 means you are producing more fissionable material "fuel" than you are using. When you move your mouse over fuel slots in the reactor UI it will show a "ratio" value which is how much has been converted so far.

The range on the nukes is very short and i can't reach any targets

You can complete a research project to upgrade the range on nukes, then you can nuke anywhere on the planet.

How long does the fallout on the world last?

Each one lasts anywhere from 2-40 days, any maps that are under a cloud of fallout will have the in-map radioactive fallout

Why do i lose relations with allies when i detonate nukes on enemies

Because even though you are eliminating an enemy nukes are still a weapon of mass destruction that results in fallout, fear, and refugees with horrific injuries.