Short answer: Yes, your employer can fire you at any time without reason at all.
BUT depending on your employment agreement it may not be a valid reason and depending on your location the employer may be responsible for paying in lieu of notice.
To know for sure you need to call the government agency in your area and ask.
How much notice does an employer have to give an employee when changing their schedule?
they must give you at least a 24hour notice.
No federal law states that you are to be given 24 hour notice prior to a change in your work schedule.
Unless you have an employment contract which specifies otherwise (chances are you do not, most employers do not use contracts) or unless local laws stipulate otherwise (chances are they do not), then no, the employer does not have to agree to allow you to work any length of time after you give notice. Notice serves to inform the employer that you will no longer be working for them after a specified date. They are by no means (with the exceptions already stated) compelled to keep you on the schedule until that date.
It is important to have good communication with your employer. Make sure to speak with the employer about your concerns and explain your expectation of notice of any changes to the schedule. The employer wants to keep employees happy, so hopefully they will make an effort to correct this problem in the future. Give them the benefit of the doubt this time and assume there was a misunderstanding.
Yes, the employer can dismiss the employee without notice at certain cercumstaces. This can be for theft.
a general notice requesting the employer to improve system of work
Yes, unless you have a contract with them that states otherwise, which you probably do not as most employment is "at will" and may be terminated by you or the company at any time with or without reason.
In what state are you employed? According to the IWC and the DLSE who enforce labor statutes and regulations in California under section 56.23.1 found here: http://www.dir.ca.gov/dlse/DLSEManual/dlse_enfcmanual.pdf 56.23.1 Occasional Changes In Schedule. The IWC has concluded that the employer must provide the employees with reasonable notice of any changes in the days or hours scheduled. Changes in the schedule are limited to “occasional” occurrences. (Statement As To The Basis). More frequent changes will result in the loss of the exemption from the 8-hour day requirements of California law. 56.23.2 Reasonable Notice Of Change In Regular Alternative Workweek Schedule. The term “reasonable notice” has not been defined by the IWC. For purposes of enforcement the DLSE will consider a one-week notice to be reasonable notice. Know Your Rights... locate the labor laws for your state. California's employment rights can all be found here: http://www.dir.ca.gov/
Lieu of notice means that your employer is paying you upfront so you do not have to work out your notice period.
It would depend on your contract, if you have to work any notice that an employer gives you. Often if you do not work what is asked, you will not keep your job.
Unless local laws specify otherwise wherever you live, an employer does not have to give you any notice.