My question is about using my own opinions in matters where it seems "Islam" just doesn't match up with the way I look at things and to follow my ideas over what the Quran and the Hadiths say. Is there any problem with me sort of "rethinking" the way Islam should be? There are a number of things that people say about Islam that make sense, but some things just don't appeal to me and I don't agree with it. So, what should I do? And does this affect me being a real Muslim?

Here is something that the Quran (which means the "Speech of Allah) says about what the believers are to do when they find something in the Quran and the Hadiths:

It is not fitting for a Believer, man or woman, when a matter has been decided by Allah and His Messenger to have any option about their decision: if any one disobeys Allah and His Messenger, he is indeed on a clearly wrong Path. [Noble Quran 33:36]

But no, by your Lord, they can have no (real) Faith, until they make you judge in all disputes between them, and find in their souls no resistance against your decisions, but accept them with the fullest conviction. [Noble Quran 4:65]

It is very important for us to know that Allah is the only one who can tell us what He wants for us in the way of worship to Him. He makes the rules and we try to do it. That is how it is described in Islam.

Again, in the Quran Allah says:

"The only Deen (way of life in religion) for Allah is the Deen of Islam." [Noble Quran 3:19]

"Whoever seeks a way of life (Deen) other than the one that Allah has prescribed (Islam), it will never be accepted from them and in the Hereafter, they will be amongst the losers." [Noble Quran 3:85]

"On this day have I perfected your religion for you, confirmed my favor upon you, and have chosen for you to submit to me in Islam (as your way of life)." [Noble Quran 5:3]

"O you who believe! Enter into Islam wholeheartedly; and follow not the footsteps of Satan; for he is to you an avowed enemy." [Noble Quran 2:208]

These are more or less the English translations from Arabic.

By the way, as Muslims we still have the original of the Arabic to compare the translations to for examination. For other religions, they do not have their originals anymore.

As regards your other statements, I would encourage you to read the Quran (at least 2 pages per day -- even though you might be very busy):
www.AllahsQuran.com/learn

The more that you read from the Book of Allah and the sayings of the messenger of Allah (Peace and blessings be upon him) the more that you will find that you are becoming better equipped to understand and apply the teachings, insha’Allah.

Remember also the nine steps to the purification of the heart that I mentioned in the story of Priests and Preachers Entering Islam:
www.YusufEstes.com

May I suggest to the seeker of truth do the following NINE STEPS to purification of the mind:

1. Clean their mind, their heart and their soul real good.

2. Clear away all the prejudices and biases.

3. Read a good translation of the meaning of the Holy Quran in a language that they can understand best.

4. Take some time.

5. Read and reflect.

6. Think and pray.

7. And keep on asking the One who created you in the first place, to guide you to the truth.

8. Keep this up for a few months. And be regular in it.

9. Above all, do not let others who are poisoned in their thinking influence you while your are in this state of "rebirth of the soul." The rest is between you and the Almighty Lord of the Universe. If you truly love Him, then He already Knows it and He will deal with each of us according to our hearts.

Allah has All Knowledge. Any good is from Allah & the mistakes were from myself.

Please pray for me and ask Allah to Forgive me. May Allah guide all of us to His Truth, Ameen.