Candace is right; this will happen a lot in the Spanish language, but it does not apply for this specific phrase. It doesn't make sense without the pronoun. Native speaker here!The acento is the second one you listed.
Siempre en mi corazon is the proper way to say it, but in Spain they will often times talk in 'shorthand' - Siempre en corazon, for example. You can usually cut off the 'yo' or 'tu' or whatever, if you are talking to someone who will obviously take it for granted that you mean me, you, or when you say always in my heart...that you are obviously talking about yourself. You will get a feel for when it is appropriate to do so