No Yes but in early phase, once more pus develops, it needs surgery Yes

Answer to the 1st question : Yes, it can. If the fissure is not treated there is a chance that it might get infected first and then lead to collection of pus. Sometimes infected fissures can form a tract and lead to fistula formation. Which in turn may lead to abscess. Ans to 2nd question : Incision and drainage (minor surgical procedure) is the mainstay of treatment of Perianal abscess. If the abscess is draining by itself from an opening then surgery may not be needed. Antibiotics are helpful in these scenarios but can't cure by themselves unless abscess is drained.

No. Fissure and perianal abscess are two different things. Yes perianal abscess if detected early and treated doesnt go for fistula