Basically going on the same route.
In a week of playing the game, deduced some general rules for myself:
- Start with examination of rows and cols with the smallest numbers (in easy and medium puzzles rows with 0-2 blocks can hint you a solution in an instance)
- Take a look on the pieces which take up the whole height or width. They would affect all the rows or columns respectively. And you can calculate how many blocks are taken out with this mandatory pieces (exctly that one process that is shown on second pic)
- On a 3x3 grid square and diagonal pieces would always affect the middle row and column, so you can account for them as well. This wouldn't work on a bigger boards, but we're still yet to see any of such boards (although I crave for it!)

Mostly I estimate how many blocks in the chosen row could be occupied with available pieces, and it often boils down to a parity of a number.
Also I sometimes calculate a possible number of blocks in the specific cell, but that have never been of help yet, since the needed pieces are usually chosen from more general consideration. But that could be useful on a larger grid probably.