Good job replacing your chain! It's a job that can done easily when you have the right tools. And it saves you some money for a mechanic too.

which can be anywhere from 3000 to 5000 kilometers so I have read.
It really depends on how you use your bicycle. If you put a lot of force on your chain (especially with climbs, but also riding in higher gears.
You know the saying "Meten is weten" (measure and you will know), which you already do with your tool.

The two hooks! No way! I have a similar tool, but always used a piece of iron wire to keep the parts together.
And I also never degreased a chain before mounting it.

You're never too old to learn!

I do have a tip that might help you too.
When I break my old chain I hang it on a nail. Then I hang the new chain right next to it. This way you can determine the length a bit faster.
Do pay attention that the old chain is a few milimeters longer.

Like this: