Trusteer Rapport is a security app that is usually recommended or mandated by services like banks and other institutions. I used to have it because Nationwide bank in the UK used it but they no longer do and I removed it. I believe you only need it if you're required to do so by a company you deal with. If you do decide to delete it the you should use the app's uninstaller, don't just delete it using Finder. If there's no uninstaller on your Mac then search for one online.
Rapportd is not related to Trusteer Rapport. Rapportd is a Mac background process that handles comms between some apple devices. You don't want to delete it.
If you're looking at Console and that's where you're seeing "more errors and exceptions" then you can ignore them. If you removed every app that kicked up a error or exception in Console then your Mac would be back to bare metal.