That sounds way too high for mask costs. You're definitely looking at 7 figures, but I don't think they've yet hit 8. Unfortunately the answer to all of your budget questions is: it depends. It's going to scale with the complexity of your requirements. Something like a custom ARM chip with heavily custom machine learning and signal processing, high speed clocking, etc, would probably need a decent sized team and a few years. On the other hand, there are tiny teams in Asia that crank out bitcoin mining ASICs like candy.

I'm going to guess at a number and say you're probably looking at $10-20MM all in.

As far as hiring good designers, you really need the relevant technical background to screen them. Assuming you need a team, I would suggest starting with someone in a director position at a large company with experience in your area of interest. They would be able to more concretely define the project and determine human resource requirements/allocation.

If your ASIC is just large but not complex (meaning lots of repeated structures), and you can get away with just a few strong designers, I would suggest hiring a consultant to help you define the project and screen candidates. EE profs at your local university might be a good start.

Feel free to shoot me an email (in my profile) if you want to describe your project in more depth and I'd be happy to offer what advice I can.