Scores are stable over time. This can be determined by statistics. It's called test-retest reliability.

You can get better at IQ tests by doing more of them and learning the patterns, right?

Yes. That is considered to "invalidate" an IQ test, but it's not usually an issue since the tests are typically administered to children.

IQ tests are basically only used in the context of individualized education plans for young school children (or for MENSA membership).

So it’s basically measuring how au fair you are with logic puzzles rather than anything particularly intrinsic.

The fundamental issue of testing is that no test can objectively determine intrinsic properties.

But no, a full IQ test done by a psychologist tests a lot more than "puzzles", including things like memory tests and even fine motor skills or hand eye coordination.

When I was tested they found I scored really high in the pattern recognition stuff and memory tests, but my writing was slow and sloppy and below average.

As part of my individualized education plan I was allowed extra time on tests as well as study aids such as text to speech tools because of this.

The ultimate purpose of the IQ tests is to get a general idea of the strengths and weaknesses in certain area.

Excellent memory, and quick intuitive problem solving, like in my case, can compensate and mask ADHD symptoms like trouble focusing. These tests helped reveal that at an early age.

I think a lot of people think of IQ tests like they're "how objectively smart are you" when really they're used to find out which areas you need help in with your education/life so we can provide kids with that support.