Convertible top will not open?

When the button flashes look at the driver info center on the dash. It should show a message and a code. From there you need a dealer level scan tool that can access the body and roof control modules to access the fault data it has. There are multiple switches and sensors that could be at fault stopping it. The only other item is fuse 25 in the junction box under the glove box. It powers the top module. Beyond that you need the info from the control modules to see what they say. You will also need the scan tool to do any repairs as the top has to be placed in different positions for sensor testing which the tool guides you though.

That means it sees an error in the control module that runs the convertible top. With that error you will need a scan tool or access to one that can do the testing that the OEM units can. There are not many that can handle that because BMW likes to keep things close. However, I suspect that the module will need to be replaced and programmed to work in your car.

The only way to open it from outside is the power latch. Either the button or on some the BMW logo, the only manual release that I know of is inside the trunk in case you get locked inside it. It likely doesn't unlock because of the top issue. The ECU doesn't know if the top is closed or open or partway through a cycle, so the trunk doesn't open.

That would be related to the other problems. With a scan tool it's possible to "talk" to the different modules and in most cases, you can look at the sensors as well. So, if you know that the top should show say 4 sensors as closed and 2 open when the top is fully locked but in scan data it shows 3 closed and 3 open you know to look at the sensor that is wrong.
They made the system much more complex than it really needed to be.

Understandable. The scan tools to do these types of things are expensive and unless you plan on using them a lot, they are not a great investment. We will await the update.