Yes and Yes.
Entrenchments started during a battle would have been dug with anything at hand. Usually bayonets and tin cups that were commonly available to the soldiers. They would have been improved later using appropriate tools if conditions warrented. An example of this would have been Grant's troops who were in the charge at 1864 Cold Harbor. When the charge failed,the troops entrenched where they were using whatever they had. Later shovels and picks were brought up and the works improved.
Entrenchments were also pre-prepared. Engineers were sent ahead to lay out the line and troops/laborers were brought in to construct them. An example of this was the Dimmock line around Petersburg constructed around 1862-3 (if my memory is correct).