I would get it out of pond water for right now. Wait until the plant has established itself before adding outdoor contaminates. The water from outdoors has all sorts of bugs and algae that would just love to be in a nice, warm house this time of year with lots of nutritious, bright artificial light and some Utric to snack on. It's very possible that your plant will be consumed by these critters if it's damaged and not able to trap prey. Also, you should probably not use that shell if it's been in a fishtank, at least not without thoroughly soaking and washing it with CP-safe water for at least 24 hours (to remove salts and other minerals.) Is your vase translucent? An opaque (preferably black) container will help discourage algae growth. Also, until the plant is in good health, remove most of the sphagnum or allow it to dry out intermittently - constantly submerged sphagnum quickly rots and becomes great algae fertilzer. Until your plant is healthy enough to compete with algae, you should be careful to inspect it and change the water regularly.
I used to have four nice jars with two varieties each of U. gibba and inflata, but I stopped paying attention to them and lost one of the inflata - the remaining three are very small now and just hanging on. I have a bunch left in my terrarium, but it's all mixed together so I don't know what any of it is. Before I messed up and neglected them, I would take them out of the water, place them on a clean plate, and spray them down with RO water to wash off algae, about once a week. It would knock off some bladders but the strands grew very vigorously in response. When I stopped washing them (and I had them in too much light) the algae took hold and strangled my growing tips.
Feeding your plant isn't necessary, and probably won't even work until it's grown new traps. If you're going to use pond water, boil it to kill off any algae. Once your plant is established and growing healthily, you can give it sphagnum and pond water, which will produce plenty of little wriggly things for the Utric to eat. While it's recovering, I'd advise to play it safe.
~Joe