how to add dropdown field to advanced view?

First off, I'm curious about why you're trying to do this in the advanced XML? It's much easier in the simplified XML but there might be something specific you're trying to accomplish by using the advanced XML. What is that?

Now, to answer your question. If I take one of the simplified XML views from the UI examples that includes dropdowns, then append ?showsource=true to the URI, I can see the advanced XML behind the dropdowns. It looks like:

<view autoCancelInterval="90" isVisible="true" objectMode="SimpleForm" onunloadCancelJobs="true" template="dashboard.html">
 <label>Simple select drop down</label>
  <module name="AccountBar" layoutPanel="appHeader"/>
  <module name="AppBar" layoutPanel="navigationHeader"/>
  <module name="Message" layoutPanel="messaging">
    <param name="filter">*</param>
    <param name="clearOnJobDispatch">False</param>
    <param name="maxSize">1</param>
  </module>
  <module name="Message" layoutPanel="messaging">
    <param name="filter">splunk.search.job</param>
    <param name="clearOnJobDispatch">True</param>
    <param name="maxSize">1</param>
  </module>
  <module name="TitleBar" layoutPanel="viewHeader">
    <param name="actionsMenuFilter">dashboard</param>
  </module>
  <module name="HiddenSearch" layoutPanel="viewHeader">
    <param name="search">index=_internal source=*metrics.log group="per_sourcetype_thruput" series=$series$ | fields eps, kb, kbps</param>
    <param name="earliest">-30d</param>
    <param name="latest">-0d</param>
      <module name="SearchSelectLister">
        <param name="staticFieldsToDisplay">
         <list>
          <param name="value">*</param>
          <param name="label">Any</param>
         </list>
       </param>
       <param name="search">index=_internal source=*metrics.log group="per_sourcetype_thruput" | top series</param>
       <param name="label">Select series</param>
       <param name="settingToCreate">series_setting</param>
       <param name="searchFieldsToDisplay">
        <list>
         <param name="value">series</param>
         <param name="label">series</param>
        </list>
       </param>
       <param name="searchWhenChanged">False</param>
        <module name="ConvertToIntention">
         <param name="settingToConvert">series_setting</param>
         <param name="intention">
           <param name="name">stringreplace</param>
           <param name="arg">
             <param name="series">
              <param name="fillOnEmpty">True</param>
              <param name="value">$target$</param>
            </param>
          </param>
         </param>
         <module name="SubmitButton">
          <param name="allowSoftSubmit">True</param>
          <param name="label">Search</param>
           <module name="JobStatus">
            <module name="EnablePreview" layoutPanel="panel_row1_col1" group="Matching events">
             <param name="groupLabel">Matching events</param>
             <param name="enable">True</param>
             <param name="display">False</param>
              <module name="SimpleResultsTable">
               <param name="count">50</param>
               <param name="drilldown">row</param>
               <param name="allowTransformedFieldSelect">True</param>
                <module name="ConvertToDrilldownSearch">
                 <module name="ViewRedirector">
                  <param name="viewTarget">flashtimeline</param>
                 </module>
                </module>
              </module>
             <module name="ViewRedirectorLink">
              <param name="viewTarget">flashtimeline</param>
             </module>
        </module>
      </module>
    </module>
  </module>
</module>

The reason i am using advanced XML is because I want to have this form-search on the left column of my dashboard, and another form-search on the right column. Or is there another way to do this (2 columns dashboard) without using advanced xml?

If you want two columns then you need to look at the attribute 'layoutPanel'

e.g

then do for two columns you need another two with the following;

layoutPanel="panel_row2_col1" layoutPanel="panel_row2_col1"