"Jeg elsker dig" can be both romantic and to a family member/friend that you hold very dear. But it's very deep feelings involved. Another way of saying "I love you" romantically is "jeg holder af dig", which means that you really care a lot about the person you're saying it to.
You can argue about that. Since both forms ("ich habe" and "ich hab") are possible and correct, you may use an apostrophe. But, as I found out, the Duden recommends to omit the apostrophe, see https://www.duden.de/sprachwissen/rechtschreibregeln/apostroph Quote: "[...] sie [solche Wörter] werden daher gewöhnlich ohne Apostroph gesetzt" (translation: they [such words] are usually used without an apothrophe). Please note the "gewöhnlich", which does not imply that using an apostrophe here is plainly wrong. But nonetheless I will strongly support the omission of the apostrophe in those cases from now on, just because it looks better and because it is correct.
For German, "Liebe" means a couple things. For example, when writing a letter you could say "Lieber Octavi Ersevi," meaning "Dear Octavi Ersevi." It also means, as you said, "Ich liebe dich" which is "I love you." You could also say "Du Liebt ihr," or " You love them." Notice the big Liebt vs the small liebe, and it's not just a conjunction thing. Go to https://www.duolingo.com/dictionary/German/liebt-lieben-verb-present+indicative+tense-third+person-singular/950d54aad87303c820e9f37fcde43bf7 for more info.
Native German here. "Du Liebt ihr" is wrong in three ways. It is "Du liebst sie", which either means You love her or You love them, "you" being singular here.
lieben (to love) is a verb, so it is spelled with a lower case "L"
liebst is 2nd person singular, which is necessary because of the "Du", while "liebt" is either 3rd person singular (as in "er liebt") or 2nd person plural (as in ihr liebt)
sie is necessary because lieben demands the accusative case (Wen liebst du?), while ihr is dative case