In theory, no. If you have everything that is required to get an ARC, the process should be smooth sailing. The problems, if they come, will come with the school not getting the list of required documents straight. Expect them to ask for one half of the documents, and then another thing two weeks later, and then an extra photo or two a week after that, etc. It’s happened with me with big organisations that have done hundreds of ARCs before.
It depends upon what you mean. Realistically, when they say they can give you ten hours now, but will increase that later, expect that to mean that they won’t increase that later. Maybe they will, but really don’t count on it. That’s what they’re trying to say to get you in the door to cover their classes. That leaves you with two possible predicaments. The first is not having enough hours, which you could possibly make up elsewhere anyway. The second is not having the legally required minimum. This could be a problem, but in practice, it’s very hard for the government to prove this and do anything about it. The school could bullshit its way through that without any problems. This happens with lots of people. Two of my best friends here don’t have the legal minimum through their ARC jobs.
By your post count, I’m assuming you’re not a newbie. As such, you must have some idea about the grey area that is anything official in Taiwan. Yes, sorting out your ARC is important, but I think you could get it done okay. Personally, if I were looking at working at a buxiban, I’d have much bigger questions on my mind. If this is the worst of your concerns, then you’re probably pretty lucky (or you may not have asked the right other questions).