We have experience with HTML, CSS, responsive web design, Bootstrap, JavaScript, jQuery, PHP, MySQL. Also, we have done projects in Wordpress, eCommerce platforms (Wordpress WooCommerce, Opencart, Prestashop), MVC frameworks (Laravel, Zend Framework). For details, please see our portfolio and/or contact us to discuss.
Please send us more information about this part, as it is not clear what we have to do: "We also have designs for a new mobile app that we want coded and connected to Wordpress admin". Do you want to develop a mobile app, Android and/or iPhone or are you referring to a mobile/responsive website?