3. To know me is to love me... everybody will interpret this their own way.
It is generally meant to mean. "if you love me then you will know me and understand me, because you love me and know me and still love me, despite my failings." That general sense.
Your last reflection is correct.
2. "seeing is believing" is the saying/idiom you are looking for.
It means people will only believe what they see. Sometimes used to cast doubt on something.
If it sounds absurd or unlikely.
1. "to be cruel to be kind" means sometimes you have to discipline people so that they do not go astray in later life, is the most common use of the phrase "you have to be cruel to be kind"
If you allow your children to run amok then it is likely that they may one day be imprisoned for life or worst, if you had disciplined them as youngsters, they have a better chance of avoiding a life of crime.
The most common situation when that phrase is used.