You may just have a bad remote. (give it a slight whack in your hand or make sure a button is not stuck)
Try removing the batteries completely from the remote (in order to disable it) and then try using the official mobile Roku Remote App. (available in Play Store or Apple Store). If the Roku behaves normally after using the mobile Remote App, then culprit is the remote.
Regarding the blinking blue light, I have noticed my Express4k+ does blink alot more than my other Roku devices when using the remote to navigate (the other units dim a bit in response to remote press, while the Express4k+ seems to actually blink and flash.)
If you purchased in a store or online, I would return unit and swap for another if you determine the remote is the issue. If you ordered online from Roku directly, perhaps @RokuDanny-R or @RokuKariza-D can help you with remote replacement.
Roku Community Streaming Expert
Just another Roku user... I am not a Roku employee.
Insignia RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941