Once I earn a Phd, is it easy to find a professor job?

No. There are many more people out there with PhDs who want to teach than there are jobs available. And if you're in a field where there's not much you can do with a PhD besides teach (like philosophy) expect to be competing with hundreds of others for a single job.

No. People who earn Ph.D. (sp.) degrees have great difficulty in finding jobs as professors. The reason is that more people earn this degree every year than there are job openings for new Ph.D.s. This is because colleges are finding it cheaper to higher low-paid part-time instructors than tenure-track professors. A part-time instructor teaches three or fewer classes at the college (9 hours maximum per week) and is paid less than $5,000 per class in most cases. Full-time, tenure-track positions at colleges pay about $40,000 per year to start in most cases, but there are very few of them available. Most of them go to the top graduates of the Ivy League Ph.D. programs. Tenure-track means that in about seven years if you have published enough books and articles, you are offered a promotion to associate professor and regular full-time employment so long as you continue to perform well. If you do not have a Ph.D. from an Ivy League University with top letters of recommendation and a dissertation which is publishable by a university press, you are very unlikely to find a tenure-track position. Instead, you will struggle all your life to find enough part-time academic jobs to pay the rent and buy cheap food. This is especially the case if your degree is in the arts, humanities, or social sciences. Sorry for the bad news, but it's better to learn it sooner than later so that you can find a career goal which offers a reasonable chance of steady employment at a good salary.

hell no Most new PhD graduates need to spend time as an underpaid post-doctoral research fellow for several years before they can become an underpaid assistant professor. Also, there are less and less tenure track positions as universities and colleges choose to use temporary adjuncts to teach classes, as they can pay them even less. If you actually did some serious non trivial research during your phd degree that made a difference in your field then you have a chance to go straight from phd student to assistant professor though.

No. Just what your chances are will depend on your subject, how good your work is, where you get your PhD, the connections you make, etc. But there are professor jobs right now that have hundreds of applicants for a single opening, and fields in which your chances of *ever* getting a tenure track professor job are <10%.