This IceCore module diagram might help here :
And to answer your questions:
iceboot is just a c file really, the firmware reports back as 'mystorm verxx' I am using the name mystorm for now however I am open to a long term name..
Yes prog from STM32 directly like BlackIce II (actually bitbanged) or have the Ice40 load it's image file from the SPI flash directly.
We will not store the bitfile in the STM32 flash moving forward, not much point in that, especially with the SPI flash attached.
I think you are asking if a synthesised core can write to the flash directly itself, if so the answer is yes..
Yes after programming the Ice40 it can switch into slave spi mode controlled by synthesis (SPI Master) running on the Ice40.
Yes I could not use QSPI due to feature limitations on the STM32F730 64 pin device, but the DSPI is capable of 200Mbit/sec more than adequate for the triple 2.4MSample per sec (or 7.2Msample/sec interleaved) ADC
The HDMI TMDS comes direct from the Ice40 (limited resolution obviously) but the HPD,CEC and I2C have to be 5 volt tolerant hence I connect them to the STM32 which supports this. We can then write a translate module in the mystorm firmware to convert data between Ice40 SPI and these protocols.