You are discovering the difference between working in academia and industry.
They told me that should not be saying anything about [the patent application] to
others until they take an action. They said they do not need to be in a hurry
because patents can not be guaranteed [granted?] to them in a few days, and it
takes years.
This is correct. Do what they say. If the competitor's patent application was submitted after your paper was published, your work might invalidate that application. But if what you published was theoretical, or proving a principle, and what they are patenting is an application of that theory or principle then it might be allowed. There is a lot of subtle, fine detail to IP law and Patent Attorneys charge big fees to deal with that. Leave this to whoever at your employer deals with the company's IP to judge whether the patent applications are a threat to their business and whether/how the 'prior art' you published can be used, now or in future, to defend against that threat.
I have some other papers that I need to publish, and these guys are
very slow and they do not understand the value of my work... What
should I do?
In academic terms, you 'need to publish' these papers because guarding your individual reputation and standing in wider academic circles is important - your worth is judged based on how many papers you publish, in which journals, where your name appears in the list of authors and how many citations it gathers in other papers. In industry, the worth of that knowledge is based on applying it to a product that customers are willing to pay for. It's more of a team game, where getting an application into the market first, and maintaining an advantage over the competition is often more valuable to your team (the employer) than publishing because a patent costs a lot to obtain and even more to defend, and, for all that papers in academic journals might burnish the company's technical credentials, they also give the competition a leg-up if they are published before the product is established in the market.
There would have been an agreement in place between you, your university and employer that allows you to write up your work in sufficient detail and share it widely enough to satisfy the requirements of your masters degree. If you think the company is now reneging on that agreement and your masters is at risk, speak with your university tutor - s/he will be able to offer advice on how to resolve that and the university can afford better lawyers than you if it comes to that.
Any IP you have developed outside the masters placement almost certainly belongs entirely to the employer and you should discuss with your boss whether/when you might be able to publish the papers. It's quite possible that they will be slow or even prevent you publishing this because it is their IP and they understand very well the value of your work in commercial terms and want to protect it.
The job offer that I have from this company is low and I do not think
they know the value of my work, so I need to change my job in a few
months. How could I manage my patent, projects, and papers?
Forget the patent - it's not your patent, it's someone else's application, and this is a matter for your employer.
Given that you feel your salary is low for your skills and experience, work on your assigned projects to the best of you ability then ask for a raise when you have demonstrated value to their business (e.g. for a year as a full-time employee). If you want to, apply to better-paying jobs in the meantime and hand in your notice when you have a firm offer that you prefer. And if you leave this company, forget publishing any papers or applying for patents based on the IP you developed while employed by them - your salary was the reward and recognition for this work.
To me, it reads as if they are valuing your work in commercial terms whereas you are placing more emphasis on the academic value. If publishing your work widely and gaining wide recognition for your individual contribution to a field is of high value to you, you may be better looking for a career in academia than in industry, and accepting that the financial reward may be lower.
