Learn Farsi: زن فضول به حریم دیگران سرک می‌کشد. - The nosy woman snoops into others' privacy.

سرک comes from سر (head) plus the diminutive suffix ـَک (-ak). Literally, it means a 'little head' or a 'quick peek'. The compound verb سرک کشیدن (literally 'to draw a little head') is a common idiom meaning 'to snoop', 'to peek', or 'to pry'.

What exactly does حریم mean in this context?

حریم (harim) refers to a personal boundary, sanctuary, or private domain. In Farsi, privacy or personal space is often expressed as حریم شخصی or, as seen here, حریم دیگران (others' personal space). Notice that it pairs with the preposition به to express intrusion into that space.

Can فضول be used on its own as a noun, or is it only an adjective?

In this sentence, it acts as an adjective modifying زن (woman), connected by the unspoken ezafe. However, فضول is frequently used as a standalone noun to mean 'a busybody'. You could drop زن entirely and just say فضول به حریم دیگران سرک می‌کشد to mean 'The busybody snoops into others' privacy'.

How would the sentence change if we added انگار (it seems / as if) to say 'It seems the nosy woman is snooping'?

You would simply place انگار (engâr) at the beginning of the sentence. Because the speaker is assuming an ongoing, factual action based on observation, the verb remains in the present indicative (سرک می‌کشد) and does not change to the subjunctive.