I easily picked up the Quran, being able to read and memorize surahs.

Obviously not indepth enough. Have you memorized the tafsir to? Thought so. How about hadith? How many? Bukhari memorized hundereds of thousands. Your at 0....

What in fact, is a real Muslim? Is it one that prays five times a day? Is it one that memorizes the Quran? Is it one that feeds the poor?

One who does the most good with what he's got. So does that stuff and excels in them.

And what if this same person commits adultery, idol worship, swears, and disrespects the elderly. Then is he still a good Muslim?

No.... Their a bad Muslim, but Muslim nevertheless, but Idol Worshipping makes you not a muslim at all.

what kind of Muslims are we if we are the type that tells people not to write "fart" or refuses to teach their children about sexual education?

The first part.... What? And kids shouldn't learn that. But people aren't kids when they hit puberty. So before that it doesn't matter to them. And so let's not add that fitnah to them before they can manage it or actually is relevant to them.

What I am trying to say is, Muslims have lost sight of the real Islam and what it means to be a real Muslim.

You just said you don't know what that is couple paragraphs up.....

I asked a question, and now I clarify, how can I become a true Muslim, one that is honest and caring, one that loves his fellow human, one that is modest and selfless?

Ask your Imam. Can't answer that for you. Just follow the sunnah to the best of your ability knowing your cercumstances. Don't become "holier than tho" because you do stuff others don't. Remeber a sahaba was an alcoholic even after Islam. And he's from the best generation. You don't know what good they do. But don't be an idiot either when it comes to blatant bad influences. Just do the right thing. It's simple as that.