I don't think you will have trouble with simple sentences. Most of the simplified characters bear some resemblance (phonetically, for example) to the original more complex characters. Some are unchanged. Every time I have asked someone fluent in Chinese whether they had trouble with the simplified vs. traditional the answer has been 'no'. Bear in mind, I was not translating classic poetry but simple survival or technical Chinese.
I have heard it said that the simplified characters are 'uglier', that they lack balance or whatever.
I don't think anyone will be insulted if you only know simplified characters, they are well aware that most learners of the Chinese language are going to be learning the language spoken in the mainland with 1.3bn people. Rather they will likely be impressed by your ability to handle hanzi.
Mandarin is the official language of Taiwan, for historical reasons (the government of CKS fled to Taiwan as the communists took over and imposed the language on the original residents), and their version is easily understood. There are a number of other dialects and languages spoken, of course, and a few very old people may still be fluent in Japanese. The majority of people actually speak a couple of other dialects as well as the official language, so there are some differences in the idioms etc. One example, which may or may not still be valid, is that in the mainland a girlfriend (or boyfriend) would be airen (爱人), but in Taiwan it meant mistress. I think it's still okay to call waitresses in Taiwan xiaojie (little miss), but less so in the mainland. Also some mainland expressions are probably a bit 'colorful' for Taiwan. The slang term for 'cool', for example, the second character of which doesn't even appear in many dictionaries.
I understand Pinyin is now taught in Taiwan as of about 10 years ago (they used to use a different transliteration system), but that won't help so much with older people.