How similar are Swedish and Norwegian language?

Yes, they are very similar. When I communicate with Norwegians, I speak/write in Swedish and they reply in Norwegian. There are a few words which are different, but most of the language is almost identical.

Can Norwegians understand Swedish?

Yes, but Norwegians are better at understanding Swedish than the other way around. In Norway there are many dialects. They differ quite a bit from each other with differing vocabulary and grammar. Many words considered Swedish are also found in many Norwegian dialects.

Is Swedish harder than Norwegian?

When it comes to Danish vs Norwegian, Norwegian is easier to understand. Their writing is the same, and there’s not a lot of difference between vocabulary and grammar either. And for Swedish vs Norwegian, Norwegian wins again. It’s a slight bit closer to English in terms of vocabulary and pronunciation.

Do Swedes speak Norwegian with Norwegians?

As a native Swedish speaker I will talk Swedish when with Norwegians and Norwegians with Swedes will usually speak Norwegian. However depending on your how comfortable you are with the respective language, you can throw in the Norwegian words you know and try to speak with a more similar melody/prosody.

Which type of Swedish is easier to understand for Danish speakers?

Danes tend to understand Norwegian better than Swedish. Some say that Norwegian is the type of Swedish you can understand =). It makes sense as the vocabulary is almost identical, so when you get the phonetical differences, it is straightforward to understand.

Can Swedes and Danes just speak their own language without effort?

Popular Scandinavian television series have spread the rumor internationally, that Swedes and Danes can just speak their own language and understand one another without making any kind of effort. The reality is a little more complicated.

Is it rude to ask someone if they speak Norwegian?

No, in itself it is not rude. You can do it in a rude way, by just ignoring the signals if the other person is not happy about it. Offer the person you talk with the choice. I would start with a Norwegian hello or good morning/day, and next try out which language sits best.