When boss tells you to make changes in the pre-production system and he/she doesn't know that to make these changes. Each change causes several problems because you have to change the database and system structure in other modules. This repeats every three or four days systematically and there is no project plan. Is this normal or my boss has not enough experience in project management? What can I do?
Your project probably had a series of problems due the way it is going; both in the technical aspect (bug count increasing, poor quality, high cost) and personal aspect (repeated extra hours, people leaving the project).
You can gather these and present them to your boss and any other person involved/affected by the project in a meeting. Asking them to tell what they feel about these issues and to brainstorm new ways of work to address them. This meeting would be similar to an Agile Retrospective. Many ideas will be raised and just a subset of them are workable right away. Thank everybody and address the workable action items to people. Repeat this meeting regularly to review the result of the action items and new issues.
Specifically to the problem of "This repeats every three or four days systematically", you can use the idea of timeboxed iterations and planning. The development team will extract from your boss as much information as possible about a subset of the visible work to do and implement it (changing scope as little as possible - i.e., only change if new information will make your work better) in a short period. Both timeframe and scope should agreed by both the development team (affirming they think they are capable delivering it in the given time) and management (affirming he wants the dev team to implement this thing and he will give both time and support to the dev team).
About the project plan, and assuming you are not talking necessarily about a document, but about a vision; I'd be open and honest with my boss and ask him the reason for building the product, into what context it will be used, what are the important that he can vision. Remember that this direct will undoubtedly change during the project, so, it is important to tell him that regular updates about stakeholders expectations are important so the team can analyze the correct direction - working together with him to deliver value.