Latvia, Lithuania and Estonia all got invited to join NATO in 2002, and joined in 2004. I would guess that Putin either wasn't too bothered at the time, because he still had the buffer of Belarus and Ukraine for the majority of Russia's borders, or more likely Russia couldn't afford to attack 3 countries spontaneously at the time, and/or it would have been a massive faff?
Do they feel the same way about any other ex ussr countries? Do they believe Belarus is a part of Russia really? Or just Ukraine?
Belarus is part of Russia, I mean it's not, but it basically is (for now). It was part of the USSR and is now run by a dictator called Lukashenko who was in the USSR and whose been in power since 1994. He relies on Putin's power and money to keep him in power, and Putin wants to keep him in power because he will do what Putin wants, so it's a win win relationship for the two of them. He's a Putin puppet. He will never join NATO and has rigged elections. Belarus did have wide spread protests after the last rigged election, but it got quashed eventually, protests were banned and the leader of the opposition got sent to prison for 18 years.
Whereas Ukraine did over get rid of their pro Russian government in 2014. Before that it was run by Yanukovych, who was Pro Russian and anti Europe, his government tried to distance themselves from relationship with the EU and increase their ties with Russia in 2013. Ukrainian people were not happy, revolted, overthrew the government and Yanukovych had to flee (to Russia). Then Russia invaded Crimea in Ukraine to "protect ethnic Russians" and has technically been at war with Ukraine ever since, so this has been simmering for a long time. Ukraine is now becoming closer to the west, and Putin does not want a Russian speaking democracy on his door step, giving Belarus ideas, especially not one in NATO. Plus he's fucking nuts.