Minecraft – way to count the number of blocks a player steps on

For this problem, you don't actually need to modify the players score when they are offline (which is possible, but finicky), you should be able to change their score as soon as they log back in.

First, create a scoreboard objective of type stat.leaveGame:

scoreboard objectives add quits stat.leaveGame

You should then have two command blocks on some kind of clock, one activated after another. In the block that is activated first, put this command:

scoreboard players set @a[score_quits_min=1] timer -1

Then, in the one that is activated second:

scoreboard players set @a[score_quits_min=1] quits 0

The quits score increments when the player leaves. So, when they log back on, it will be at 1 and their timer score will be set to -1. Their quits score then has to be set back to 0, so that it can be used for the next logout and also so that timer isn't repeatedly set to -1,

Yep, /fill allows you to specify keep as an [oldBlockHandling] mode, and thus only replace air. Try this:

/fill X1 Y1 Z1 X2 Y2 Z2 fire 0 keep