Has anyone got any experience in using this suite ( Ext JS, Sencha Touch, Ext Designer) and webspeed ?
Yes - extjs. Works fine. Couple of quirks that are extjs specific where they want some some extra properties. ABL dataset stuff forces some extra layers in the json if you need more than a single table in the returned data, but nothing that can't be worked around.
Need to make sure your http headers and responses are correct; esp. if you decide to use REST calls.