Hi Arnold
I Have made some Changes
Try This..
<apex:page sidebar="false" standardController="Account" recordSetVar="accounts" tabstyle="account" extensions="DisplayContact">
<!--<img src="{!$Resource.OnePiece}" />-->

<script>
var lastRow;
function highlight(elem){
    if(lastRow != undefined)
        elem.style.fontWeight = 'bold';
        lastRow = elem;
}
</script>

<apex:form id="frm" >
<apex:pageBlock title="Account" id="accounts" mode="edit">
   <apex:inlineEditSupport showOnEdit="saveButton, cancelButton"
                 hideOnEdit="editButton" event="ondblclick"
                    changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
      <apex:pageBlockTable value="{!accounts}" var="a" id="list" rules="rows" onRowClick="highlight(this);">
      
        <apex:column headerValue="Account Name">
            <apex:commandLink rerender="contactDetails" value=" {!a.Name}" action="{!ContactLists}">
                <apex:param name="id" value="{!a.id}"/>
            </apex:commandLink>
        </apex:column>
        
        <apex:column value="{!a.type}" />
        <apex:column value="{!a.billingstreet}"/>
        <apex:column value="{!a.billingCity}" />
        <apex:column value="{!a.billingCountry}" />
        <apex:column value="{!a.billingPostalCode}"/>
        <apex:column value="{!a.createdById}"/>
        
      </apex:pageBlockTable>
      <center>
      <!--<apex:commandButton value="Show Contacts"/>-->
      <apex:commandButton value="Hide Contacts" action="{!EditContact}" rerender="contactDetails" />
      </center>
</apex:pageBlock>


<apex:pageBlock title="Contact" id="contacts">
   <apex:outputPanel id="contactDetails" >
     <apex:pageBlockTable value="{!conList}" var="con" id="conlist" title="Contact">
         <apex:column headervalue="First Name">
             <apex:outputField value="{!con.FirstName}">
                 <apex:inlineEditSupport showOnEdit="saveButton, cancelButton"
                        hideOnEdit="editButton" event="ondblclick"
                        changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
              </apex:outputField>   
         </apex:column>
         <apex:column headervalue="Last Name">
             <apex:outputField value="{!con.LastName}">
                 <apex:inlineEditSupport showOnEdit="saveButton, cancelButton"
                        hideOnEdit="editButton" event="ondblclick"
                        changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
              </apex:outputField>   
         </apex:column>
         <apex:Column headervalue="phone">
             <apex:outputField value="{!con.phone}">
                 <apex:inlineEditSupport showOnEdit="saveButton, cancelButton"
                        hideOnEdit="test" event="ondblclick"
                        changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
             </apex:outputField>    
         </apex:column>
         <apex:Column headervalue="Email">
             <apex:outputField value="{!con.Email}">
                 <apex:inlineEditSupport showOnEdit="test"
                        hideOnEdit="editButton" event="ondblclick"
                        changedStyleClass="myBoldClass" resetFunction="resetInlineEdit"/>
             </apex:outputField >    
         </apex:Column>
         
         <apex:column>
             <apex:commandLink onclick="javascript.void(0);" id="test"> Edit </apex:commandLink>             
         </apex:column>                
     </apex:pageBlockTable>
     <center><apex:commandButton value="Add New Contact" rendered="{!showResults}" action="{!AddnewCont}"/>
         <apex:commandButton value="Save" rendered="{!showResults}" action="{!QuickSave}"/>
     </center>
   </apex:outputPanel>
</apex:pageBlock>
   </apex:form>
</apex:page>

=============================Class========================


public with sharing class DisplayContact {

    public DisplayContact(ApexPages.StandardSetController controller) {

    }


    public List<Contact> conList {get;set;}
    public List<Account> accList{get;set;}
    public Contact con{get; set;}
    public Boolean showResults {get; set;}
     
    
    public PageReference ContactLists()
    {
    showResults = true;
    if(ApexPages.currentPage().getParameters().get('id') != null)
      conList = [Select id,Name,firstname,lastname,Phone,Email from contact where accountId =: ApexPages.currentPage().getParameters().get('id')];
      accList = [Select id From Account Where Id=:ApexPages.currentPage().getParameters().get('id')];
      System.debug('*****' + conList);
      System.debug('*****' + accList);
     return null;
    }   
    
    
    public PageReference EditContact(){
      conList = null;
      PageReference hide = new PageReference('https://c.ap0.visual.force.com/apex/AccountSearchContact');   
      showResults = false;   
      return null;
    }
    public PageReference AddnewCont(){
    
        if(ApexPages.currentPage().getParameters().get('id') != null)
              
              
              accList = [Select id From Account Where Id=:ApexPages.currentPage().getParameters().get('id')];
                  for(Account a: accList ){
                  PageReference addnew = new PageReference('https://ap.salesforce.com/003/e?retURL=%2F' + a.Id+ '&accid='+a.Id);
                  return addnew;
      }
              
        return null;
}
        
        
    
    public PageReference Edit(){
    
    if(ApexPages.currentPage().getParameters().get('id') != null)
            
              conList = [Select id,Name,Phone,Email, AccountId from Contact where AccountId =: ApexPages.currentPage().getParameters().get('id')];
              
               System.debug('&&'+conList);
                  for(Contact c: conList){
                  PageReference addnew = new PageReference('https://ap.salesforce.com/' + c.Id );
                  return addnew;
        }
              
        return null;

    }
}