Agreed. I have checked Toyota Indus website, but could not find 5w-30. May be, they have not updated the details on their website.
Yes. Correct. But still, fully synthetic would be the best choice.
As said by @fastian04 , I think you can use it, and have it stamped on the warranty booklet.
Its abnormal. There seems something fishy. In any case, it must be less than 100 Kms IMO (whatsoever is the reason).