Hi, Sigrid. "it is uncommon in Japan to give out advice to others" is not true, but 「~たらどうですか」 and 「~ほうがいいですよ」 are not 謙遜語（けんそんご) = humble language, 丁寧語（ていねいご）=polite language, nor 敬語（けいご）=Honorific language. http://www.guidetojapanese.org/learn/grammar/honorific So if you use these language to person who is elder than you, higher position in the office, and you meet first time or do not have friendly relationship with that person, then one may feel you are impolite. If you speak to those who are elder or at higher position, I will use 「～されたほうがよいのではないでしょうか」、「～されたほうがよいのではないかと思います」、「～てはいかがでしょうか？」

Yes, they are used for giving advice. I never once heared about giving advice being impolite in Japan (I lived there for one and a half year). And those kind of sentences are used a lot in daily life.