I would say that both, you and your partner, are equally correct. Even though I don’t fully understand what is meant with “is tested in every step” in your partner’s approach. I think you should pick the approach that is easiest for you to implement (automatize) and maintain. Both approaches seem like they could be automated. It also seems that you have pretty much all the use cases covered. Are you overanalyzing this?
If I read between the lines, I think you’re asking that if you should add many steps to a single test case vs. one step (use case) per test case. This is a classic problem. One step per test case gives you better understanding where the defects are, but if there are many steps in total that means also plenty of test cases. You should really choose the approach that is best suited for you. For example in unit testing people tend to put only one use case (or assertion) per test case, but there’s nothing really wrong if you don’t do it that way. You should considered making these tests as easy and fast to execute as possible.
About styles verification: Do you feel that it is necessary? I would prioritize functionality above look and feel. You could verify styles by just looking at the application in question. Automating those tests can be quite a chore and hard to maintain. I would say that almost in every case it’s not worth it.
In addition I would like to say, that validation logic could be easier to test with unit tests.