The difference is that by starting a sentence with the object ("DAS glauben wir"), you emphasize the object, i.e. here the word "das". Possible contexts might be: "Oh yes, we believe THAT, but not all the other things you told us" or a construction like "That is what we believe".
"Glauben" can be used with a person (e.g. I believe the man/him) or with a thing (e.g. I believe his story/that). After "glauben", a noun/pronoun referring to a person is in the dative case, but a noun/pronoun referring to a thing is in the accusative case.
Ich glaube dem Mann (dative).
Ich glaube das (accusative).
Ich glaube dem Mann (dative) das (accusative).
In addition, "glauben" can be used with a preposition: glauben an (= to believe in), e.g. "Ich glaube an Gott" (I believe in God); "Ich glaube an seine Unschuld" (I believe in his innocence). After "glauben an", you always have to use the accusative case, regardless of whether you're talking about believing in a person or a thing.
Where did you get those words. "is what"? "That we believe." or "We believe that." It looks as though you are translating "Das ist was wir glauben." although they seem to add an extra word themselves. "Das ist das, was wir glauben." or "Das ist es, was wir glauben." http://www.reverso.net/translationresults.aspx?lang=ENdirection=english-german
That would be "so dass wir glauben" or "damit wir glauben" http://www.reverso.net/translationresults.aspx?lang=EN=english-german http://dictionary.reverso.net/german-english/so%20dass http://dictionary.reverso.net/german-english/damit
Nope, it wouldn't be acceptable since "dass" is a conjunction, whereas "das" is a pronoun. Also, one slight correction: It would be "Ich glaube, dass du recht hast," since "dass" marks the start of a subordinate clause, which requires that the verb goes at the end of the clause. :)
Peut-être. In English, it is so rare to use the direct object to begin a sentence, but in German, it seems to be quite common and it would probably be less likely to say, "Wir glauben das." Our book teaches that one only needs to be sure the verb is in the second position. There are several ways to say, "I have German on Monday." You can begin with the direct object or the day, as long as "have I" is the verb-subject order. I am not sure that it is for emphasis, but it would seem so for one who is used to the English word order. In English,"That, we believe." would surely put more emphasis on the word "that."