She's only 6 months old, that's good. That means she's still technically a puppy and there's still time to correct this behavior. Since she's a Jack Russell/Poodle cross, I seriously doubt she's stupid - those are two very trainable, usually bright breeds. The shadow-chasing could just be puppy play, but most likely it's boredom - Jack Russels have a lot of energy and require a lot of exercise and stimulation. What kind of toys does the dog have to play with? What kinds of activities do you do with your dog? Have you tried clicker training?
http://www.clickandtreat.com/ That web site has some good resources for clicker training - it's behaviorism-based training that associates a sound (a click produced by a little plastic clicker) with very specific behaviors that you mark with the sound, and then reward with a treat. Most dogs learn incredibly quickly, even my Cooper (who, while extremely sweet, is not the brightest bulb in the box - but she does sit, stay, come, down, heel, touch, sing, jump, etc., all through clicker training). When you're not actively paying attention to her, make sure she has stimulating toys like <a href="http://www.petsmart.com/global/product_detail.jsp?PRODUCT%3C%3Eprd_id=845524441775350&ASSORTMENT%3C%3East_id=2534374302023689&FOLDER%3C%3Efolder_id=2534374302026218&bmUID=1107960723684">Kongs</a> or a <a href="http://www.petsmart.com/global/product_detail.jsp?PRODUCT%3C%3Eprd_id=845524441778374&ASSORTMENT%3C%3East_id=2534374302023689&FOLDER%3C%3Efolder_id=2534374302026219&bmUID=1107960779457">Molecuball</a>, or even just a rag with treats in it tied in many many knots - that's Coop's favorite toy, keeps her occupied for hours.
Since she is so young, the submissive peeing is most likely something she'll grow out of. But she'll grow out of it faster if you make sure she has some confidence (reward training automatically helps that) and she'll be less likely to get into trouble and get yelled at (a confidence-dropper) if you make sure she has plenty of activities to keep her occupied.