K.H.
You have several issus adressed that you want to change , I think you need to do 1 at a time , get that issue sorted and then move on to the next. The 2 issues are more than likely connected , he is waking because he is probably hungry. I would sort the food issue first , at 11 months he can have quite a variety of foods , cooked pasta in sauces (you could make a tomato based sauce and add veggies to it and use a hand blender to make it a little smoother) , scrambled eggs , pancakes , bagels with cream cheese. Things like chicken you can cut up and then cook it so it stays moist , mashed potatoes , sweet potato fries , soft fruits such as banana slices , strawberries , clementine pieces etc. Don't let him see that you are anxious about his eating because they do pick up on this and will become all the more fussy , let him eat what you are eating (within reason) , cut it up small so he can pick it up and put it in his mouth , he needs to learn how to chew and move food around his mouth & purees just arn't going to teach him that. You will be surprised at what they can eat with just 4 teeth! Once you have the food side of it sorted then move on to the sleep , at his age he needs to be going to bed around 7/7.30pm and sleeping for a good 12 hrs with one 2 hr nap in the day , maybe 3 hrs at a push , when you are ready to start the sleep issue I would wake him up at 7am regardless of what time he went to bed , keep him awake until at least noon then let him have his nap , wake him by 3 at the latest and then put him to bed at 7 , have a bedtime routine (bath , pj's , milk , bed) and stick to the same night after night so he learns the routine , it will take time , he will cause a fuss but he is young enough to learn these changes , he's a baby and he cannot dictate the rules , as the parent you have to let him know what goes on in the house and what he eats and when , and when he goes to bed.
Good luck.