Well it's 51 minutes later, and I got to the third bullet point :D

EDIT: I tried to focus on readability here. Things could be quite a bit more concise but that requires firmer grasp of interactions between >>=, <$>, and point-free functions.

Here's what I have so far:

    {-# LANGUAGE OverloadedStrings #-}
    module Main where
    
    import Prelude hiding (appendFile)
    import Data.Monoid ((<>))
    import Network.Wreq
    import Control.Lens
    import Control.Concurrent.Async
    import Data.ByteString.Lazy (ByteString, appendFile)
    
    main = do
      urls <- promptUserURLs
      responses <- mapConcurrently get urls
      let responseBodys = fmap (view responseBody) responses
          responseInfos  = fmap (\(url,body) -> (take 5 url, body)) (zip urls responseBodys)
          httpUrls = filter (\(url,_) -> url == "http:") responseInfos
          httpsUrls = filter (\(url,_) -> url == "https") responseInfos
      mapM_ (appendFile "output1.txt") httpUrls
      exampleSiteResponses <- mapConcurrently get httpUrls
      let exampleSiteResponses' = fmap (view responseBody) exampleSiteResponses
      mapM_ (appendFile "output2.txt") exampleSiteResponses

    promptUserURLs :: IO [String]
    promptUserURLs = go []
      where go :: [String] -> IO [String]
            go urls = do
              line <- getLine
              if line == ("q" :: String)
                then return urls
                else go (urls <> [line]) -- lol, this is a very bad way to snoc