Use the /scoreboard command

It auto-increments every time that player kills another player. Use dummy instead if you want a counter only commands change.

Run /scoreboard objectives setdisplay sidebar <objective>. You can also target list (tab menu) or belowName.

The sidebar only lists entries with a score. Run /scoreboard players set <player> <objective> 0 to make them appear.

set forces an exact value, add increases by an amount, remove decreases. All take a player, objective, and number.

Yes. Put /scoreboard players add @p kills 1 in a command block on a clock or a button to drive counters automatically.

Run /scoreboard objectives remove <objective>. This removes it from every display slot and deletes all stored scores.

Names must be unique and cannot contain spaces. Java allows letters, numbers, and the symbols - + . and _; Bedrock still caps the name at 16 characters while Java removed that limit in 1.18. A space or a duplicate name is the usual cause. Wrong criterion spelling fails too; criteria are case sensitive.

The objective name is fixed once created, but the display name is separate. Add a JSON text component as the third argument, like /scoreboard objectives add kills playerKillCount {"text":"Kills","color":"gold"}, or set it later with objectives modify <name> displayname.

Yes. Any entity UUID or a fake player name (any string) can hold a score. Use a fake name like #total kills 0 to store global counters that never show as a real player.

Objectives and scores persist in level data, but the setdisplay slot does not. Re-run /scoreboard objectives setdisplay sidebar <objective> on load, or put it in a function tagged minecraft:load.

Use the target selector with scores, for example /execute if entity @p[scores={kills=10..}] run say done. The 10.. range means 10 or more; ..5 means 5 or less.