$keyword = trim($_GET["Keyword"]);
if (!empty($keyword)) {
$if_statement = ($keyword == $Product->keyword);
}

$shopByStore = $_GET["store"];
if (!empty($shopByStore)) {
$if_statement = ($if_statement && $shopByStore == $Product->store);
}

// plus 7 more GET methods retrieving potential user input for the $if_statement variable.

$XMLproducts = simplexml_load_file("products.xml");
foreach($XMLproducts->product as $Product) {

if ($if_statement) { // the problem lies here
echo $Product->name;
}}

if($Product->something) {}  //this is meaningless and will throw and error
//if you define $Product->something here