I am a native English speaker from the U.S, and I just said "experience going to a Japanese school" a few times out loud. I hear the "to" every time. It may be that the speaker did not annunciate that particular word when pronouncing it, so it was hard to hear. Or perhaps, he/she was from a different region/country and, therefore, has a different accent.

"And" is best used in the middle of sentences to join two nouns or two independent clauses. It is rarely used to start a sentence in formal writing. "In addition" is good at the start of a sentence, to signal that the sentence will add information related to the previous sentence.

You would probably use 'in addition' in place of 'also' more of then you would use it in place of 'and'. For example, 'John plays the guitar and piano. In addition, he is a good singer'. You could also word the second sentence, 'Also, he is a good singer.' With 'and' it would most likely be all in one sentence, 'John plays the guitar, piano, and he's a good singer.' Overall, I would say 'in addition' is something you will use much more rarely than 'and'. One last thing, people sometimes use 'Additionally' instead of 'In addition', so that is an option as well. They are interchangeable.