Infinitive A is infinitive B
Here are some sentences in the pattern of "inf. A is inf.B".

1. To be kind to the enemy is to be cruel to the people.

﹉I think I know its meaning by logic: if you are kind to the enemy, you are actually cruel to the people.﹉

2. To see is to believe.

﹉ One should only believe something after they have seen it themselves. ﹉

[ Do I understand it rightly?]

[ By the way, this sentence comes from a teaching material. I have not yet found it (as a saying) in dictionaries. A similar one that is widely known is "seeing is believing". Do you think this is all the same as the well-known one?]

3. To know me is to love me.

﹉ This sentence gets me confused. ﹉

[Should I understand it as 1) as along as you get to know me, you will certainly begin to love me or 2) If you try to know me(better), I'll see it as the reflection that you love me. 3)...

Question

Infinitive A is infinitive B
Here are some sentences in the pattern of "inf. A is inf.B".

1. To be kind to the enemy is to be cruel to the people.

﹉I think I know its meaning by logic: if you are kind to the enemy, you are actually cruel to the people.﹉

2. To see is to believe.

﹉ One should only believe something after they have seen it themselves. ﹉

[ Do I understand it rightly?]

[ By the way, this sentence comes from a teaching material. I have not yet found it (as a saying) in dictionaries. A similar one that is widely known is "seeing is believing". Do you think this is all the same as the well-known one?]

3. To know me is to love me.

﹉ This sentence gets me confused. ﹉

[Should I understand it as 1) as along as you get to know me, you will certainly begin to love me or 2) If you try to know me(better), I'll see it as the reflection that you love me. 3)...

Answer

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.

Answer

1  yes
2 I know this as "seeing is believing" You are more likely to believe what you see yourself.
3 I think this comes from an old song.
To know him is to love him.
I suppose it means something like the act of truly  knowing someone leads to loving them, but it is more about emotion.
Perhaps hearing the song will help.
https://www.youtube.com/watch?v=DCnUsInBQws
There is a more modern version from Amy Whitehouse which you might prefer.

Answer

To be x is to be y to the z.
In your example being kind to the enemy will result in the enemy be/continuing to be cruel to the people.