Is using Amazon's advertising for a children's ebook effective?

No it is not. Unless you are a big name you place yourself next to strong competitors that are supported by big budgets. Start small with friends, friends of friends, get reviwes, create a blog become known and maybe spend some money with FB ads. If you have the budget print some copies and fight for your space with readers clubs etc. It is a tough business with a lot of competition and therefore you must work in order to be noticed .

It can be, if you niche down. Generally, you are going to spend a lot if you target keywords like "Halloween Book," but if your book is specifically about a kid who is making a Jack O Lantern, target some things like "Jack O Lantern Book." Of course, you won't get the volume, but you will get a better conversion rate. Through the last 6 months of Amazon ads I have sold over $1MM that can be attributed to ad clicks and have spent less than $30k.

Its TOUGH. I marketed a childrens book a long, long time ago when their advertising was less evolved.

My suggestions: Locate top mommy bloggers and pitch 'how to' related content for your book. Offer guest blogging and pitch 10- ideas for that given blogger. All it takes is one YES for you to have a flood of targeted , referral traffic. I can share how this is done if you would like

I believe amazon is not that good for books.
Only sellers can run Amazon ad campaigns. If you only have a print edition which has been slurped in, you cannot run an ad campaign. You would have to create a seller store-front, sell the book through that, and then run a campaign as that seller and only for the things sold on that store-front.
You can read more here: https://kmhalpern.com/2019/04/08/why-not-to-use-amazon-ads-for-your-book/
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath