Can I use SELECTION mode on FeatureLayer from ArcGIS.com Webmap in ESRI JS API

The webmap returns a featureLayer already instantiated. I haven't tried changing the mode to instantiate a featureLayer with mode selection, but it makes sense that you lose symbology and popups because you set those when instantiating.

Solution: I have queried (queryTask) against the featureLayer url based on user drawn polygon (or user click, hover, etc), and then set the features (polygons) returned from the query to an outline of aqua blue, and then added them to the graphic layer -- so it looks like they are selected.

Meanwhile, I'm displaying the featureLayer from the web map underneath that shows the symbology, popups, etc that were configured in the webmap. Of course, you could achieve the same effect with a tile cache and you wouldn't be limited by the 1000 record max limit -- that may be better for you. I turned the visible scale to only show close in for the webmap.

Here's a sample -- (adapted and untested)

//goes inside your your onclick function here
if (geom !== null) {
    var query = new esri.tasks.Query(),
        queryTask = new esri.tasks.QueryTask(params.parcelServiceName); //featureLayer url
    query.geometry = geom;
    query.returnGeometry = true;
    query.outFields = ["*"];
    queryTask.execute(query, function (results) {
        highlightPolygons(results);
    }, function (error) {
        //vgis.app.jQueryUIAlert(vgis.config.APP_STRINGS.ERROR_CONDITION);
    });
}
else {
    //vgis.app.jQueryUIAlert(vgis.config.CUSTOM_STRINGS.PARCEL_NO_RESULTS);
}

//function to add aqua highlighting outline
function highlightPolygons(results) {
    var geom,
        graphic,
        symbol = new esri.symbol.SimpleFillSymbol(esri.symbol.SimpleFillSymbol.STYLE_SOLID,
            new esri.symbol.SimpleLineSymbol(esri.symbol.SimpleLineSymbol.STYLE_SOLID, new dojo.Color([0, 255, 255, 1.0]), 2),
            new dojo.Color([255, 255, 25, 0.0]));
    map.graphics.clear();
    dojo.forEach(results.features, function (key, value) {
        geom = value.geometry;
        graphic = new esri.Graphic(geom, symbol);
        map.add(graphic);
    });
}