Learn English – How to pronounce an English /t/ sound smoothly at the end of a word

"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)

As James K said, this doesn't have anything to do with the spelling.

Different accents of English have different patterns for the use of "dark l" vs. "light l". As you mentioned, some accents are even described as having only one of these sounds. Accents with "both" sounds are often described as actually having a "gradient" of "darker" vs. "lighter" /l/s in different environments. So this is a pretty complicated question.

In general, there seems to be a tendency for "dark l" sounds to be used more often in American accents than in British accents.

In the British "Received Pronunciation" accent of English that is often taught to learners, "light l" is used before a vowel sound, even when the /l/ comes at the end of a word or after a stressed vowel. This accent would have "light l" in "killer", "bellicose", and "pullup". (I don't know if the "light l" in "pullup" might be a bit darker than the light l used in other contexts; that sounds somewhat plausible to me.)

In certain American English accents, "dark l" is used before consonants, and also word-finally, even when a vowel follows, but "light l" is used before a vowel in most word-medial contexts. These accents would have "light l" in "bellicose", but because "pullup" is a compound, I think it might have dark l. I'm also not sure how words like ""killer" are treated in these accents.

In other American English accents (like mine), it seems that "dark l" is used whenever the /l/ is not at the start of a metrical "foot" (either as the very first sound, as in "lucky", or as an element of the onset cluster in the first syllable of the foot, as in "climbing"). So I have "dark l" in killer, bellicose and pullup because the /l/ is not at the start of a foot, but I have "light l" in words like illiterate, illuminate, crystallography, collect where the /l/ is at the start of a stressed syllable.

I quoted some sources in my answer to a related ELU question: L in the middle of a word: dark l or light l?