on my opinion, they are separated (by comma) sentences.... "I see" is like to say "ok" or "now I know" "ok, you like breakfast" the comma changes the meaning of the sentence
"I see" is a tad bit more complex than "ok". Your example is the right definition though. However, in English you wouldn't pause after saying "I see" in this context, where as you woukd using ok. That would sound weird. There is a famous line from the movie Spaceballs where one of the characters says, "I see your schwartz is as big as mine." In the script there is no comma.
Most of the time you will never use a comma after it. Almost every sentence that I can think of where you might use it, you could often omit it. The same can be said for "ok" in most cases, but ok sounds a lot better with a pause.
По-русски мы не говорим "Вы любите завтрак". Это предложение не правильное. You like breakfast - Вам нравится завтрак - or - Вам очень нравится завтрак. Можно сказать Вы любите бутерброд, or Вы любите борщ. Слово ЛЮБИТЕ можно употребить по отношению к какому-нибудь блюду, но не к завтраку или к обеду в целом. Можно сказать "Вы любите завтракать" (this verb) - You like having breakfast. In Russian the sentence is wrong!