Project Plan 365 app will not move your task automatically if you have the same resource on two parallel tasks. 

The application tells you that you have an overallocated resource by making the entire resource font with red in Resource Sheet view.

If you want tasks to be in sequence, you need to link the tasks and specify a predecessor.

In order to add a hyperlink to a task, you need to apply first the Hyperlink table from the menu Project - Table. Then you can change the Hyperlink Address field.

You can also use the Insert column feature. Insert Hyperlink and Hyperlink Address field in Gantt Chart, then edit them.

For a file from local device, in Hyperlink Address field insert the path to the file like this: file:///C:/Users/UserName/Desktop/PDFName.pdf

For a file from cloud or web address, in Hyperlink Address field insert the path to the file like this:
https://docs.google.com

In Hyperlink field add the name of your file.

To move the whole task: Hover over the first part of the split task.

The cursor changes to a four-way arrow.

Drag the bar left to start earlier or drag it right to start later.