Hello @Donnie_Prather, welcome to the forum!
You can add tasks to additional projects from the detail pane. Just below the due date you will see the current project, and below that there is an option to add to projects. Once it has been added to the other project you have the option to click the x on the current project to remove it.
To get all of the field entries to carry over, you’ll need to ensure that all of your fields in the current task have been added to the org library and added to the new project, specifically from the library. You can add a field to the library by clicking the dropdown menu next to the field name, selecting edit field, and then clicking the box at the bottom that says add to library.
This can also be done on multiple tasks at once by bulk selecting them and using the clipboard with the + button on the bottom navigation. This will give you the same Add to projects option as described above, or the ability to move them to another project by selecting the pencil icon next to the current one.