I am BSc student. When I was in the fourth semester (end of the second year), I did my course project and submitted it to my professor. His efforts in order to publish it really shocked me. It was just a course project and I already had a conference paper out of it. I know the article was so foolish and basic but he is insisting on publishing it. After two rejections he is submitting it to another journal. Does this journal count this rejections as negative points for the authors? If I am going to submit any paper to this journal in the future do they count this rejections?
Rejections are not necessarily a negative when submitting to a new journal. Of course, it means a careful editor will take an extra careful look at the manuscript before accepting it for review. They key point is, however, that when submitting a previously rejected manuscript it is necessary to, first, be upfront with the rejection and the reasons for it, and, second, to provide clear details on how the previous reviews have been used to improve the manuscript for the current submission. So, clearly, of one simply submit the same manuscript over and over again, yes, there is a chance someone may accept it in the end, but it is very poor work ethics to do so. A manuscript that has been rejected and significantly improved from comments received and additional work done, will have a pretty good chance of being published. As an editor you can then see indications of what may be key issues with the paper. This does not mean, as some seem to think, that submitting half-baked manuscripts and have reviewers beat them into order is the way to write good papers so there are fine lines of good conduct which have to be followed.
As for holding a rejection against you: No, not unless there are repeated sloppy submissions. But even then, every manuscript receives an independent check to see if it is of sufficient quality. A bad reputation just means you will raise flags with editors whenever you submit. And, once will not create a reputation.
I have never heard of a journal holding rejected manuscripts against the authors. Editors likely keep track informally of problem authors such that if an author is consistently submitting low quality work they may be more likely to desk reject the work than bother reviewers with it. That said, one or two low quality submissions would not be problematic.
The UK research councils have started to implement a waiting period for low quality grant submissions. Basically, if you submit two low quality grant applications in a row on sequential deadlines, you will be barred from submitting another application on the next deadline. Once the waiting period is over, the issue is forgotten. The penalty is pretty small since it is pretty hard, if not impossible, to rapidly come up with three good funding proposals. Having a mandated few month break is probably a good thing. This is relatively new and some day publishers may follow suit, but as of now, no publisher imposes such a model.
To summarise, if the PI thinks there is a reasonable chance of publication, then a few rejections (less than a dozen) will not hurt your reputation or future chance of publishing other material.