Have I correctly used 'take,' 'lightly,' and 'these' in this sentence?

The English is correct, though "teenage romantic relationships and heartbreaks" seems a preferable word order. However, the overall meaning seems illogical to me. The fact that they are a normal part of teenage life does not seem to be a reason to take them more seriously.

If I rewrite the sentence as follows, will it be acceptable?

Parents should not lightly take romantic relationships and heartbreaks, which are a normal part of teenage life.

RommelThey should not lightly take relationships and heartbreaks, which are a normal part of teenage life.

"should not lightly take" is not idiomatic. The natural pattern is "should not take ~ lightly". Your revised sentence, for me, still seems to suggest, albeit not quite as strongly, that these things should be taken more seriously because they are a normal

Would it be logical now if I rewrote the sentence as follows?

Teenage romantic relationships and heartbreaks are a normal part of teenage life, and/but parents should not take these lightly.

RommelTeenage romantic relationships and heartbreaks are a normal part of teenage life, and/but parents should not take these lightly.

With "but", I think the sentence works. You might consider removing the first "Teenage" as it is implied by the second.

Would it be acceptable, too, if I made the following revision?

Parents should not take romantic relationships and heartbreaks lightly even if/although these are considered a normal part of teenage life.

RommelParents should not take romantic relationships and heartbreaks lightly even if/although these are considered a normal part of teenage life.

In that sentence I would use "even though". Consider a comma after "lightly".

Here I would be inclined to reinsert "teenage" before "romantic relationships". This is because it now could be read initially as