Hey there! So here’s my insights to your questions:
Fiverr mentions this about it: There is a one-day waiting period between test retakes. You may only take a test twice within a three-month period.
It won’t per se. Some tests are mandatory for certain categories. For the categories where it’s not necessary, it might help your profile/gig in order to communicate to buyers that (to a certain extent) you practice what you preach and can instill trust. For example, saying you’ll write an article in perfect English but the test shows a score of 4/10 that decreases your credibility. However, some buyers rather look at your portfolio for example and don’t care that much about the tests. It’s subjective but in my eyes it can’t hurt to have a good score on your profile.
The tests do not affect your ranking/promoting at all. I believe Fiverr doesn’t filter between profiles with and without tests.
This is only true depending on the gig category I think. As I said above, you can only publish a gig then when you’ve taken the compulsory test. But whether it’s mandatory that will be communicated very clearly by Fiverr. So if you have another gig that doesn’t have a compulsory test, you can still publish that one. But it all depends on your field etc.
Hope this helped!