Translation:I think that test is probably easy.
As others have pointed out - not actually the casual form of です. Better thought of as a declarative marker at the end of the sentence that makes it assertive (thus reducing politeness). In some relative clauses, you must use だ to help disambiguate the sentence. Sometimes だ can be used in place of です, but it really is better to think of them as two separate beasts.
This link might be handy: http://www.guidetojapanese.org/learn/category/grammar-guide/page/5/ (see section "「です」 is NOT the same as 「だ」")
Not exactly the same. For instance you could not use desu in that sentence, but you would need to use da, even if using the polite form. It's worth looking into more. For instance, even in casual speech, saying sou da is more forceful than sou desu. In this case, unless you wanted to really emphasise your point, you'd just say sou. Just remember that even in casual speech, you can't always just switch desu out for da.
As a general rule that is correct.
There are some exceptions, namely when the first half of a sentence is a subordinate clause, connected to the main sentence by conjunctions such as が (but), ので or から (because). In a way, you're still only putting ～ます or です at the end of a sentence, it just might not be the final end of the sentence.
E.g. 友達（ともだち）と一緒（いっしょ）に公園（こうえん）に行くつもりですが、彼は風邪（かぜ）をひいていますので、今日は行けません。 -- I want to go to the park with my friend, but because he has caught a cold, we can't go today.