Minecraft 1.7.10 commands to 1.13?

I am creating a Nacht der Untoten remake with my friends and I was wondering how to make these old commands I used in a previous map in 1.7.10 work in the server we have now in 1.13

/scoreboard objectives add zombie stat.killEntity.Zombie zombie

/scoreboard objectives setdisplay sidebar zombie

/testfor @a[score_zombie=0]

/scoreboard players set @a zombie 10

/scoreboard players remove @p zombie 20

/testfor @p[score_zombie_min=15]

I tried putting these exact commands into 1.13, however they didn't work. I tried to research but to no avail.

Solution 1:

First command:

/scoreboard objectives add zombie minecraft.killed:minecraft.zombie zombie

Third command:

/execute if entity @a[scores={zombie=..0}] run <chained command>

Fifth command:

/execute if entity @p[scores={zombie=15..}] run <chained command>

All other commands work identically in Minecraft 1.13