Love is a complicated thing and there are a range of emotions that accompany it.
That said, terms like "eye love" or "love through eyes" are not readily understandable in English; you would almost assuredly have to explain what you meant. You defined eye love as:
two people look at each other and somehow they feel that the other likes them, or is interested in them
English does have many words that describe this sort of thing. One that comes to mind is infatuation; from NOAD:
infatuate (v.) (be infatuated with)
be inspired with an intense but short-lived passion or admiration for : she is infatuated with a handsome police chief
There is also moonstruck, which NOAD defines as:
unable to think or act normally, esp. because of being in love.
So, I might say something like, "Tommy saw my daughter from across the cafeteria, and was moonstruck. By Friday, he had worked up enough courage to ask her out."
There is also the idiom head over heels, which has an interesting usage note at TFD:
head over heels (in love)
to be in love with someone very much : It's obvious they're head over heels in love with each other.
Usage notes: often used with fall to describe the beginning of a relationship: They met at a nightclub and instantly fell head over heels for one another.
There's also the term puppy love, which NOAD calls "an intense but relatively shallow romantic attachment, typically associated with adolescents." And there's the noun crush, which NOAD says is:
crush (n.) a brief but intense infatuation for someone, esp. someone unattainable or inappropriate : she did have a crush on Dr. Russell.
On the other hand, your definition of "love through mouth" as:
people who are not be interested [in each other] the first time they see each other but after they talk to each other many times, love is developed over time
I wouldn't call this "love through mouth" or even "love over conversation." You are describing a deeper love that evolves slowly over time. While English has a few terms that describe that burst of emotions that you call "eye love," I can't think of anything that describes this more gently developing love. In fact, if I were describe it, I'd probably use a term that describe infatuation, and negate the term:
- Linda and Bob's relationship was no puppy love; they were good friends for a long time before they started to develop romantic feelings toward each other.
There are a few words you can use to described the intermediate feelings between first getting to know someone, and first falling in love with someone. A couple that come to mind are warmth and fondness; such words could be used in a conversation that goes something like this one:
Sara: I'm being to develop a real fondness for Dave.
Tina: Are you falling in love with him?
Sara: I don't know if I'd call it "love" yet, but I'm definitely warming up to the thought.
If I was describing the difference between these two concepts to my teenagers, I wouldn't use "eye" and "mouth"; instead, I would use "heart" and "brain":
This is easier said than done, but don't fall in love with your heart, fall in love with your brain.
where heart refers to early, impulsive emotions, and brain refers to a more deliberate and thoughtful process.