You're probably ending up evaluating the JavaScript before the "edit.html" page has loaded. Try this:
// I'm assuming the real path is something like file:///android_asset/edit.html
edit.loadUrl("edit.html");
edit.setWebViewClient(new WebViewClient() {
@Override
public void onPageFinished(WebView view, String url) {
if (Uri.parse(url).getPath() == "edit.html") {
view.loadUrl("javascript:SetEdits('" + name+"','" + email + "','" +
picture + "','" + date + "')");
}
}