Do you think 'love' exists outside of human experience?

No. But I don't need to know this in order to think this, because it wouldn't change my thinking if it could be shown that love does exist outside of human experience, so your question seems irrelevant.

"Unobservable" refers to abstract concepts, and philosophers use that term to distinguish it from "unobserved" -- something that should be able to be observed if we only had the senses or tools to do it. A geometric proof is an example of an unobservable meaning in that might be impossible to observe in nature (such as true vacuum is), but it can nonetheless be shown to be true, so it belongs to the set of things in the world that can be shown to exist by using language. (Wittgenstein's truth-proposition framework.)

Other unobservable things, such as the meaning of love and death to an individual, do not belong to that set of things that can be proven to exist using language because whether or not they do exist are irrelevant to further thinking about them. Existence is not a relevant question for an abstraction such as love, but communicating what one means by love still may matter nonetheless, which means that it is still part of the world.

Do you believe there are no such things as abstractions in the world? If so, can you prove it?

Lazy thinking imposes restrictions usually by misusing language.  Misusing language is akin to using language as a crutch, much like we complain about religious people using faith as a crutch. Lazy thinkers fail to imagine meaning beyond present definitions of symbols, and they fail to appreciate how the definitions of the symbols they been given by others must necessarily restrict their ability to think about the world. Non-lazy thinkers, which are rare, are those use their recognition of the limits of language to generalize beyond those limits and thereby make new discoveries about the world.

Do you think 'love' is completely amorphous and freeform, and everyone's experience of it is completely original and unique?

No, I don't. Uniqueness is not a relevant concept to my understanding of love. (I'm not sure why you keep bringing it up.) Whether love is the same or different for each individual has nothing to do with wanting to think about and communicate one's own personal experience of it. It is enough that I think that each individual being is unique. (Which can be proven using only simple characteristics such as time and space to show that at least in those two dimensions no two individual beings are the same.) That's why you can't universally define "love" as "sexual attraction." (Again, how many people can you find who really think those two words mean the very same thing? I know you won't find many philosophers or other people who have really thought deeply on this subject who do.)  

There certainly are stories, concepts, roles, etc, that are common enough to be recognizable and predictable. But that's not important to our discussion here. What matters in many cases are not the odds of prediction, but individual, unique experiences at hand. Although there are billions of people in the world, the only experience of it that I can answer to is my own. I'm the only one who will die my own death, and the bio-chemical description of that death will be irrelevant to my experience of it, even if it is relevant to my experience of others' deaths.

As a banker once told me regarding his lack of trust in portfolio risk management techniques, "When you're the one who's diving head-first into a pond, it doesn't really matter what the average depth is, does it?"