Help with my devices possibly hacked w dev

Is it possible to deploy config onto a device (or devices) without the owner's knowledge in order to gain access to their information? I suspect that this has been done to my devices via our wireless network as my iPhone iPad and mini all get redirected when I browse and behave strangely. I am not part of any enterprise or mdm, no server to my knowledge.

Is there a way to check? No profile shows in my settings but I understand that a profile can be hidden if needed. In my diagnostics data there are strange listings but how do I know what is legit and what is not? Please help as I do not know programming and I am at a loss? Apple retail staff were unable to assist as they said that they are not versed in dev. Thanks in advance for any help.