If your chosen method for updating was over the air on your iPad, then try connecting your device to iTunes (computer) and restore it. This might help a bit. Before restoring, make sure there's a most recent backup, either to iCloud or to iTunes.
Hello and welcome to the forum! Please tell us which iOS version is now installed on your iPad 2? The current version is 9.3.1, and iOS 10 should be released this fall - your device is already on the lower end of the compatibility list and possibly will not qualify to go to the next upgrade.
Your machine was released 5 years ago and much has changed - see the spreadsheet below showing some specs on the iPad 2 vs. several of the most recent iDevices (Source). Thus, if you want to go the the most recent iOS upgrades and also use apps designed for the more modern hardware/software, then a 'new' (or newer) iPad may be in your future?
Also, take a look at this recent Article on upgrading to iOS 9.x - many of the issues you raise are discussed. Also, downgrading to an earlier iOS may not be possible depending on whether Apple has signed off the version, e.g. for an iPad 2 (Wi-Fi only) the current signed versions seem to be the current ones (see second image below - Source). Dave
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Glad to help along w/ Johanna - I went from an iPad 2 (bought 2011 and used for 3 1/2 yrs) to the Air 2 and loved the transition - the current iPad Air 2 offerings come w/ 16 or 64 GB capacity - I picked the latter and would strongly recommend that amount of storage. Good luck - there are many iPad options, as shown below from Apple's website. Dave
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