1. I'm not going to give up on love.

2. I'm not going to give up love.
[Are both the same in meaning? Is there any meaningful differences between them?]

3. I want to get over my limitations.
4. I want to get over my limits.
[Can we use both 'limitations' and 'limits'? Which one is commonly used?]

1 and 2 are not the same in meaning.

give up on -- to stop trying to do something with someone or something, such as being friendly, giving advice, managing, etc. I gave up on jogging. My knees went bad.

give up
to quit; to quit trying. I give up! I won't press this further. Are you going to give up or keep fighting?

https://idioms.thefreedictionary.com/Give+up+on

I don't see much difference between 3 and 4, but I have never heard or read the phrasing in 4.

1. "I'm not going to give up on love" means that you will continue to believe in and pursue love, despite any challenges or setbacks you may face.

2. "I'm not going to give up love" could have a different meaning. It could suggest that you are not willing to surrender or let go of the love you have for someone or a specific relationship, regardless of the circumstances.

So, while both sentences express determination and a refusal to abandon the idea of love, there is a subtle difference in meaning between the two.

3. Both "limitations" and "limits" can be used, but they carry slightly different connotations.

"I want to get over my limitations" implies that you want to overcome the restrictions or barriers set by yourself or external factors.

On the other hand, "I want to get over my limits" suggests that you want to surpass or push beyond what you believe are your own capabilities or boundaries.

In terms of common usage, both terms are used, but "limitations" is more commonly employed when referring to personal obstacles or restrictions.