It is my understanding (not a native Spanish speaker) that they can be used like "believe (creer)" and "think (pensar)" in English, so there's many sentences where they can be used interchangeably, but many where they can't. Here's some examples:
"I think you can do it" or "I believe you can do it." (pienso que lo puedas hacer/creo que lo puedas hacer). In that sentence the words "think" and "believe" carry essentially the same meaning, but take the sentence "I believe in you (creo en tú) ," for example. It wouldn't make sense to say "I think in you (pienso en tú)"
Also, on a side note, "pienso en tú" or something like "él piensa en ella" doesn't really translate literally for an English speaker, the phrases mean "I think of you" and "he thinks of her" respectively. So even though "pienso en tú" is grammatically correct if you were trying to say "I think of you", it wouldn't carry the same meaning as "creo en tú (I believe in you)."
I'd like to offer a couple of minor corrections to your post, if I may.
- In your examples, "you" is the object of the sentence, not its subject. So instead of "tú", you'd use the object pronoun
ti: creer en ti, pensar en ti.
(Note that the object pronoun "me" is "mí", with an accent. That's to distinguish it from "mi", no accent, which means "my". There's no accent needed for "ti", because the Spanish word for "your" is "tu" [again, no accent].)
- The main difference between "think" and "believe", in either language, is the degree of certainty you attach to the statement.
With Spanish, that means that affirmative statements containing "pensar" are likely to use the subjunctive mood, whereas affirmative "creer" statements never do. (It's the difference between "I think she might be married," as opposed to "I believe she's married.")
Note that negative statements (no pensar, no creer) would almost always use the subjunctive, at least in Spanish. But again, the difference is in the degree of certainly you are assigning to the statement.
To my understanding, you can use either one interchangeably in most cases. But you got to be careful how you interpret it; in this instance, for example, you have to interpret it as "I think...", even though it says 'creo'.
In case my understanding is not correct, I hope native Spanish speaking members would kindly correct me.
Mahsazet, since no one responded, I'll tell you about using "that," but I don't have time to look up a reference for you. You are right that in spoken English, we do sometimes leave out the word "that," for example, "I think (that) you are pretty." But you would notice it if you were diagramming a sentence in an English class, where the parts of sentences and their structure are taught. You can probably find a reference by searching for "English grammar, dependent clauses and phrases used as direct objects." In this case, there is a group of words used as the direct object of the verb "think." ("I" is the subject, "think" is the verb, and what is thought (the rest of that sentence) is the direct object, introduced by the "transition " word, "that." I will end with another example: "I hope that you understand!" :-)
The word 'that' is necessary for proper English. While without it it may make the point, but it is not good English.