Generally, speed is preferred above precision while playing a TTRPG—don’t make other people wait unnecessarily, close enough is good enough! However, if your table prefers precise rulings rather than fast but “good enough” ones, use the options below as a reference.
Diagonal Spaces
Treating diagonal spaces as adjacent is the default assumption, as it tends to be easier and faster (though it can cause some spatial “weirdness” that some may not prefer). Instead, you can treat diagonals as not adjacent at all or count every other diagonal as adjacent (fiddly, but a good balance).
It’s up to your table, but whatever the heroes can do (moving or attacking diagonally), monsters can do as well.
Cones & Lines
For a cone, start at the character and extend X spaces outward. The cone can be up to X spaces wide at the farthest edge (you can make it narrower than X, but not wider).
For a line, starting from the character, extend the area up to X spaces in a single direction (you can make it shorter, but not longer), and 1 space wide. If a space is at least halfway covered by the cone or line, it is included in the effect.