Can iDevices be compromised? Hacked? Have r.a.ts installed? Can certain apps be controlled and not other, like chrome?

As far as I can gather online, all iDevices are very secure. Is this true? My devices are not jailbroken, but I am still concerned. Has anyone else had there device's lock screen open for no reason, or been asked repeatedly to re-enter passwords they never entered? Or have Chrome block recently visited sites? Do the data log on my device hold any useful information?