Learn Finnish: Minä rakastan sinua, ja sinä rakastat minua.

In Finnish, certain verbs always require their object (the person or thing receiving the action) to be in the partitive case. The verb rakastaa (to love) is one of these. Because you are directing an ongoing emotion at someone, "you" must become the partitive sinua, and "me" becomes the partitive minua.

How are the forms sinua and minua made?

Personal pronouns have slightly irregular stems in the partitive case. Instead of just adding a letter to the end of minä (I) and sinä (you), the stems change to minu- and sinu-. Then, you add the partitive ending -a to get minua (me) and sinua (you).

Do I have to include the subject pronouns Minä and sinä, or could I just say Rakastan sinua, ja rakastat minua?

You can definitely drop them! Because the verb endings (-n in rakastan and -t in rakastat) already tell us exactly who is doing the action, leaving out minä and sinä is perfectly correct and very common in spoken Finnish. Including them here just adds a bit of romantic emphasis: "I love you, and you love me."