I am using woodmart theme. when i use header simplified it does not display.Also top menu bar is not displaying any custom menu. Please tell me what the actual problem is?
No, your data will not be affected. You can take a complete backup of the website before deactivating the plugins and switching the themes.
If the issue still continues then leave all the third party plugins deactivated and provide admin panel login details of the website to check it myself and help you out accordingly.