"harmonic" and "superman" have /r/ in standard American English
Most American English speakers have a "rhotic" accent, which means they do not generally drop "r" in any position. (A minority of American English speakers have a non-rhotic accent, where the consonant /r/ does not occur before another consonant or at the end of a word before a pause, but this feature generally only occurs in specific regions. Speakers from certain regions may have even more complicated "mixed" accents that show sporadic and unpredictable use of rhotic and non-rhotic pronunciations due to dialect mixing.)
Dropping the "r" in "harmonic" and "superman" would not be standard in a rhotic accent.
advanced listener's note: rhotic speakers do sometimes drop "r"s in other words
I would not recommend trying to drop the /r/ in any words if you are a learner aiming to speak with a rhotic accent.
But, advanced students of English might find it helpful for listening purposes to be aware of a tendency for native speakers of rhotic accents to drop /r/ in certain fairly restricted contexts.
This is generally only possible in words that have more than one /r/, and it is most common in unstressed syllables. Example words with the droppable "r" capitalized: beRserk, suRprise, paRticular. Dropping the /r/ in words like this is never mandatory, and for some words, certain speakers might consider dropping the /r/ to sound informal or uneducated.
You can read a description of the general phenomenon here: "R-Dissimilation in English", by Nancy Hall ( 2007)