public class myArcoExtension {
     private final Arco__c webarco;
     public myArcoExtension(ApexPages.StandardController stdController) {
         webarco = (Arco__c) stdController.getRecord();
         attach = new Attachment();
         attach2 = new Attachment();
     }

     public myArcoExtension() {}

     public PageReference saveArco() {
       Savepoint sp = Database.setSavePoint();  
       try {
             insert(webarco);
             upload();
             upload2();
         } catch (System.DMLException e) {
             ApexPages.addMessages(e);
             /*reset the values*/
             webarco.Id = null;
             attach = new Attachment();
             attach2 = new Attachment();

             Database.rollback(sp);
             return null;
         }
         PageReference p = Page.informacion_enviada;
         p.setRedirect(true);
         return p;
     }

     public String parentId {
         get;
         set;
     }
     public Attachment attach {
         get;
         set;
     }

     public ApexPages.Pagereference upload() {
         attach.ParentId = webarco.id;
         insert attach;
         return new ApexPages.Standardcontroller(attach).view();
     }

     public String parentId2 {
         get;
         set;
     }
     public Attachment attach2 {
         get;
         set;
     }

     public ApexPages.Pagereference upload2() {
         attach2.ParentId = webarco.id;
         insert attach2;
         return new ApexPages.Standardcontroller(attach2).view();
     }

     /* Clase testMethod para validar el código y cubrir el porcentaje de cobertura */
     public static testMethod void myTest() {
         Arco__c arco = new Arco__c();
         arco.Nombre__c = 'Emmanuel';
         arco.Apellidos__c = 'Corona';
         arco.Email__c = 'ecorona@mcmtelecom.com.mx';
         insert arco;

         //Create the controller
         ApexPages.StandardController sc = new ApexPages.StandardController(arco);

         //Create the instances of the controller
         myArcoExtension myPageTest = new myArcoExtension();

         myArcoExtension myPageTestSC = new myArcoExtension(sc);
         myPageTestSC.saveArco();

         Attachment attachment = new Attachment();
         attachment.Name = 'Unit Test Attachment';
         attachment.Body = Blob.valueOf('Unit Test Attachment Body');

         myPageTestSC.attach = attachment;
         myPageTestSC.upload();

         Attachment attachment2 = new Attachment();
         attachment2.Name = 'Unit Test Attachment 2';
         attachment2.Body = Blob.valueOf('Unit Test Attachment Body 2');

         myPageTestSC.attach2 = attachment2;
         myPageTestSC.upload2();
     }
 }

 1.Well your code doesnt check whether user has uploaded a file or not and directly does and insert hence you get an error that is catched by try catch "body and header are missing and are not required". You can have a null check in saveAcro method and give a relevant error message.

2."next if they select the files but some field is wrong the page refresh and now the files are missing so if the user try to upload them again we get a error message about the id": this is because you have try catch inplace and hence records get inserted to the point where exception occurs. TO control this you have to add rollback support which I already did in your code