I don't think you need to worry... but like I wrote - allowing entry is up to the immigration officer. There are no official limit to how many times you can enter on VOA. Unless the IO have another reason to deny you entry, you will be fine.
That's up to the Immigration officer. However they are unlikely to deny an entry on VOA, since denial is often made if they suspect anyone to try and live in Thailand without a proper visa. Something that would be somewhat impossible to do since you'd have to leave every 15th day with VOA.
most likely not. Each embassy have the estimated process time listed on their webpage. But I'd say you should count on at least some workdays (not weekend) for the process... In the end it might take some more day, so you should plan for that.