I thought it was also "I like you". And typical "I love you": "Я тебе кохаю"...
Yeah, it's kind of tricky since люблю translates to like in most sentences...
"I like you" is ти мені подобаєшся.
When talking about food e.g. "I like ice cream" it can be interchanged "Я люблю морозиво" or "Мені подобається морозиво". Same as in English, "I love ice cream" and "I like ice cream" are more or less on the same footing, "love" is just a bit exaggerated.
While the difference between "I like you" and "I love you" is REALLY BIG :) Same in Ukrainian.
When I was a child, I asked my granny how to say I love you and she said it was "Я тебе люблю". Is this correct also, or no?
Yes, and it's actually as common as "Я люблю тебе" if not more common.
I guess to utter the word "люблю" is stressful in a moment one makes such a confession, so one leaves it till the end leaving more time to muster the courage :) An example from my life, when one of my friends decided to tell the other about their feelings and ended up saying "Я тебе... еееееее" and not being able to finish the sentence :D It became an internal meme :)
However, it's pretty common to use this word order even in non-stressful situations like telling it to your family members, so maybe I'm wrong :)