Does the job market desperately need accountants/CPA's?

There will always be demand for CPAs, but it follows the larger business demand cycle (more companies growing and making more revenue usually correlates to more CPAs needed to account for said revenue). Places with more businesses will likely have higher demands (eg, CA and NY will likelier have higher demands for CPAs than flyover states). You can use sites like Glassdoor to look up starting salaries for CPAs in your area to get a sense of what is realistic.

Yes - if you can make it through the first couple of years and get your CPA, you will have lots of job opportunities!

I wouldn't say firms will be coming to you but my experience both as a graduate and working in firms is that the larger firms in the area around your college will recruit from your school. The Big 4 will have higher number of positions available but I would expect you to have access to many options. The number of offers you get is going to be based on your grades, your recommendations, your activities outside of class, how well you interview., etc.

As far as career opportunities, I think CPA is a great field. All businesses need accountants and many companies need CPAs to perform audit functions. I've been very happy with the breadth of experiences I've had as a CPA and I've learned a lot about how businesses in different industries make money and what makes an efficient operation. This type of understanding is very valuable to companies so you're options after some years of experience are definitely more wide open than other professions.

Large accounting firms recruit on campus for students working towards their CPA and they often have multiple job openings. You will still have to participate in networking events, keep your grades up, and apply, but the job opportunities are out there.

As far as salary, you will probably start out around $50,000-$60,000 in an accounting firm. Large accounting firms do a lot of salary research and make very reasonable offers. With this said there is some room for negotiation, but not name your own price.