The three-cell network clue
The network clue leads to WEB. Trace WEB from row 4, column 4, then move down to row 5, column 4 and right to row 5, column 5. The letters read W, E, B in that order. It is a compact route with one turn, spanning two rows and two columns, so it makes a useful first confirmation without exposing much of the board.
For an exact check, the coordinate transcript is: 1 at row 4, column 4; 2 at row 5, column 4; 3 at row 5, column 5. This path starts on a cell with four open orthogonal neighbors and ends on a cell with two. After assigning these three cells, 17 open cells remain for the other answers.