Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
Since your apps are not downloading, I'd recommend to update it using your computer. This way, it will download and install a fresh update. First on your iPad, go to Settings > iCloud. Then turn off Find My iPad. Enter your iCloud password ***** asked.
Then download and install latest iTunes on your computer from here --> http://www.apple.com/itunes/download/
After downloading iTunes, make sure you install it by opening the downloaded file and following onscreen instructions. After installing iTunes, open iTunes. Then connect the iPad to your computer. iTunes will recognize it. If asked to restore from backup or setup it as new iPad, select setup it as new iPad. Then select your iPad icon at the upper left, next to Music, Movies etc icons.
This will bring the Summary screen of iPad. Now, click " Backup Now" button and make sure "To This Computer" is selected there. This will backup the entire iPad to your computer. Once the backup is completed, click Update button and this will download and install the update. It may take a while to (up to 3 hours for decent internet connection) to download and install the update. When the update is being downloaded, you will see a Download button (a downward arrow at top right of iTunes. Click it to see time remaining)
Installing update this way will also other apps downloading issues. Please let me know if that didn't work, so I will continue to help you