I have had instances of people deleting my applications (purposedly or unpurposedly) and it's a real annoyance to get them back, plus you lose all of your data. Is there a way to password protect the removal of applications, maybe through the use of a Cydia tweak?
No need for a jailbreak. Simply go into Settings>General>Restrictions and don't allow "Deleting Apps". Restrictions are protected using a password just like your lock passcode (although it can be a different code if you would like).