These are five minipuzzles, each using some of the 16 words in the given bank.
Some of the words can have their first letters removed to form words related to the given emoji: [s]CAR, [g]HOST, [b]EAST, [t]WEED.
The highlighted cells (the first letters of the new words) spell CHEW.
Three of the words can be placed into the white boxes here, and then have two more letters added in the indicated location to form something clued by the word on the right:
The pairs of letters spell out the answer, CARESS.
Three of the five-letter words can fit into the given blanks, where each Greek letter consistently represents a single letter in the word:
δζγβζ = GENIE
εβγζγ = LINEN
ηζγβα = DENIM
These seven letters, put in order of their corresponding Greek letters, spell out MINGLED.
Three of the words can be placed in the blanks on the left, so that when the indicated letter is changed and moved, it creates a new word as clued on the right.
The old and new letters, in Greek-letter order, spell out WIESEL. (This doesn't seem as 'wordlike' as the others... it could refer to Nobel laureate Elie Wiesel?)
We can place our last three words into the last three locations marked with a ↦:
The bits on the right side of the dropped letter spell out pairs related to the clues on the right: SIEGFRIED and ROY, TOM and JERRY, and A and T. (Perhaps there should've been an extra T there, to make the mobile network AT&T?)
Three new words can be placed in the remaining blanks to form pairs relating to the clue on the left side:
The marked letters of the newly-placed words spell out SOD.
Now, placing the minipuzzle answers in the bottom blanks,
the highlighted letters spell out CHAINED.