Each pair of definitions is for two words, where the second word is the first word with an extra letter added somewhere (example: band & brand). The length of the short word in each pair is provided.
1) low in fuel content & to gain knowledge (4 letters)
2) a small vessel for liquids & essential (4 letters)
3) a low or open slipper & malicious gossip (6 letters)
4) a mark used to indicate the place where something is to be inserted & a floor covering (5 letters)