Starting on line 133 of the cart.ascx page you set the visible property = false for the rows you want to hide. For example, see the following highlighted in yellow to hide the shipping:
<tr runat="server" id="trShipping" visible = "false">
<td align="right" class="SmithProdtext">Shipping Fee :</td>
<td></td>
<td align="right" class="SmithProdtext">
<%
String shippingFee = GetShippingFee();
if (String.Compare(shippingFee, "TBD", true) == 0 || String.Compare(shippingFee, "Free", true) == 0)
{ %>
<%=String.Format("{0:c}", shippingFee)%>
<%}
else
{ %>
<%=String.Format("{0:c}", Convert.ToDouble(shippingFee))%>
<%}%>
</td>
</tr>
<tr runat="server" id="trHandling">
<td align="right" class="SmithProdtext">Handling Charge :</td>
<td></td>
<td align="right" class="SmithProdtext"><%=String.Format("{0:C}", GetHandlingCharge())%> </td>
</tr>