I am currently studying to convert to Judaism and was wondering, since the daily prayers are centered around the idea that the one praying is in fact jewish, are there any rabinnical suggestions for prayer by those in the process of studying for conversion, or to just pray from the heart as I have?

In principle praying from the heart is enough. However a colleague of mine, Rabbi Yoel Schwartz, has compiled a few prayers that he recommends to all non-Jews. Here they are:

Basic Suggested Prayers That Are Appropriate For Everyone to Recite Daily

In the Morning, Upon Awakening

(Modeh Ani) I gratefully thank You, Living and Eternal King, for You have returned my soul within me with compassion-abundant is Your faithfulness. I also thank you for your having prepared for people the necessities for their lives and for your having given them the wisdom to recognize Your greatness and to know how to fulfill their purpose in life.

Hear O Israel: HASHEM is our G-d, HASHEM is One. And you should love your G-d with all your heart, with all your soul and with all your might. And you shall know today and have put it before your heart that G-d is HASHEM and there is none other than Him. And (eventually) G-d will be king over all the world. On that day G-d will be one and His name will be one.

In the Evening before retiring

Hear O Israel: HASHEM is our G-d, HASHEM is One.

I thank you God for all the kindnesses that you did with us (and in particular for——that you did for me today.

I request your forgivness if I have sinned or erred before you. I forgive anyone who has Harmed me and I request that you influence the hearts of anyone that I might have harmed that they should also forgive me. Before any important activity it is advisable to say

In the name of G-d we shall do and be successful

Before any medical procedure

May it be the will of G-d that this procedure should bring healing?

Grace after the main meal of the day

Blessed are You, King of the Universe, Who feeds the whole world with His goodness, pleasantness, grace and mercy. He gives bread to all flesh and the world is full of His Mercy. Due to His great goodness, we have never lacked and will never be in need of food forever. His great Name feeds and gives everyone his livelihood, does good to everyone, and prepares food for all those that He has created. Blessed be You, G-d, who sustains all. He who makes peace and harmony in His heights should also make peace among us, and the whole world.