I'm hearing this word a lot in Japanese drama and anime. What is the literal meaning of it? Does it have a Kanji form? What root(s) does it contain (I think there is a する in the second half of it? What about the もし part?)?
What is the literal meaning of it?
A literal translation will sound very awkward: (just) if doing. In any case, it is an expression of supposition about something that may be possible. Hence, "perhaps".
Does it have a Kanji form?
若しかして (perhaps even 若しか為て), but it will usually be written in hiragana.
While not recognized as modern readings, the following characters have all historically been glossed as mosi in various 漢文 texts: 仍, 假, 儻, 卽, 如, 或, 爲, 由, 皆, 縦, 脱, 苟, 設, 謂, and 頗.
What root(s) does it contain
Adverb mosi + interrogative partical ka + verb s- + particle -te. The particle ka strengthens the interrogative ("if") sense of mosi.
Just for the record, there are other compounds of mosi-ka, including "mosika sitara" and "mosika suru to".
What about the もし part?)?
An adverb meaning "if".