If you don't understand, I'm sorry. I'll try to clarify as much as possible.
I only finished 2nd Grade Korean, so I might not be able to help a lot, but here's what I think....
...of course you should all know the vowels are short, not long. e.g. (-ham-) is not the ham you eat. It's pronounced as (-h(ah)m-).
It's just used differently depending on the flow of language. This is probably advanced (unless you know japanese. It is very similar.)to understand....
sa-rang-han-da - most likely used to say that someone is in love with some one, or have crush on someone. OR, said to the person (or thing) in a way like a bit indirect because you have to put the nouns.
e.g....
nan nuhl sa-rang-han-da - I(nan) love(sa-rang-han-da) you(nuhl).
jae-neun jae-reul sa-rang-han-da - he/she(jae-neun) loves(sa-rang-han-da) him/her(jae-reul)
but most of the times, I translate this as "To be loving something/someone". But then again, I can be wrong.
sa-rang-ham-ni-da - mostly written than spoken. hmm.... not so sure. I hardly say "ni-da", since, I think, it is used mostly as "informational". if you know what I mean...
sa-rang-hae - When you say this while talking to a person or group, you don't have to say "you" or "you all". the word "hae" directly points to the person or group you are talking to. This is a familiar term, meaning you say this to people who you are friendly with and/or if you are superior over them.
sa-rang-hae-yo - Same as saranghae. except this is Formal. The word "yo" at the end of most of sentences makes it formal.
Examples of Formal endings.
"-ham-ni-da." when the sentence is giving something like information
"-ham-ni-ka?" used when questioning. (In Japanese, it similar to "desu-ka".)
"-ha-ne-yo." (-ha-) comes from (ha-da) which means "to do" so it pretty much means: "...(am/is/are) (doing or verb)..."
"-hea-yo." As I said above, this is more direct to the person you are talking to. It's like making the verb into an adjective... so sa-rang-hae-yo(when it means I love you.) makes "love" describe how you feel about the person you are talking to.
things like gat-chi-il-hae-yo(let's work together), it's just talking(or asking) directly to the person(or group) to work with you.
The thing about the sentence ending with -yo is that it can be a question from also.
"sa-rang-hae-yo." can mean "I love you.", but if it is "... (eul/reul) sa-rang-hae-yo?" can mean "Do you love ..." in question form, it is asking directly about the person you are talking to.
Just in case you are wondering what (-neun) and (-reul) meant in the first example,
(-neun), or (-eun) is same as (is/am). If you want to say (are), it would be (-deul-eun) because (They) is plural, and the word (-deul-) makes it plural.
good example would be (geu-neun) and (geu-deul-eun). (geu-neun) means (He is) while (geu-deul-eun) makes it (They are), but it can also mean (Those men/boys are). If you speak spanish, it similar to difference between el and ellos.
(-reul), or (-eul) makes it possessive. so (geu-reul) means (him). while (geu-deul-eul) means (them) or (those men/ boys). And yes, the (-deul-) rule is the same.
*If you want to say she, or her, it is (geu-nyuh-neun)she and (geu-nyuh-reul)her. (-deul-) rule would be (geu-nyuh-deul-eun)Those women are , and(geu-nyuh-deul-eul)Those women*
P.S.
Someone correct me if I'm wrong. I need to re-learn it my self... =_=