can i start reading on my kindle and then continue on my ipad

Since "Kindle" is the common denominator here, you might stand a better chance of getting an answer on Amazon's Kindle support site.

It does appear that the Kindle app has the ability to back up annotations, but I have no idea if that actually includes book marks, or if the two devices will synchronize.

Yes, I do it as well between my Kindle, iPad and Android phone. I would note that in order for it to work between the Kindle and another device, you need to turn on the wifi connection on the Kindle, at least temporarily, so it can connect and tell your Kindle account where you are in your book. I don't typically leave my wifi on when using the Kindle because of the battery drain, so I have to remember to turn it on for a minute before I'm done using it.

Same thing if you use the Kindle app on your iPad and then want to pick up again on Kindle - you need the wifi on to sync, then turn it off you prefer.

One other note - sometimes the devices (if already connected to wifi) will sync automatically. Other times I find I need to bring up the menu and tell it to sync.

Yes. You definitely can. I do this all the time. I have a Kindle, Kindle Fire, Evo, and iPad. I freely move between all of these devices, and it remember where I was each time. It's nice.

Yes I am. It works well.

I'm not aware of a setting that allows you to sync to the page you are on. I think this is the just the way it is.