Is the US allowed to have nuclear weapons but not other countries? If other countries try to get them, they should be invaded?

you mean like england, russia, france, pakistan, south africa, idia, israel, china

so when do all the invasions start?

Countries deemed to be peaceful and responsible are allowed to have nuclear weapons for their own defense and many already do.

The US (1945), Russia (1949), UK (1952), France (1960), China (1964), India (1974), Pakistan (mid 1980s) and North Korea (2006) are all confirmed nuclear armed states.

Israel almost certainly has some nuclear weapons as well, but it's never been confirmed. South Africa developed nuclear weapons in the 1980s, but abandoned them in the 1990s.

In addition there are many states that could, if they wanted, acquire nukes quite easily. Germany, South Korea, Japan, Brazil and Saudi Arabia are the most likely candidates.

North Korea acquired nuclear weapons and they were never invaded. It's not really ABOUT nukes - it's about the threat to the region and whether the country can be brought to heel easily. China and maybe even Russia would be against an invasion of North Korea. Iran? Nobody's friends with them - and they've got two very powerful enemies in Israel and Saudi Arabia.

Because we have a stable system of government with checks and balances. I'd be OK with other countries, like Japan, having nukes. It depends on the country.