Front fender, P clips will possibly work.

Brake levers, yes the ones you mentioned will work, I use the 550's but I wished I used the latest Brompton brake levers. The reason is the Brompton brake lever has the housing and cables exit the lever at an angle that is conducive to the Brompton. With the 550's the housing has sharper bends which doesn't help in braking. Not the end of the world but if you have to buy levers anyway.

For the back brake, just buy the Brompton it works well and fits perfect.

Your bar and stem look like it approximates the height of the M bar, so that is the cable length I would use. You can always cut it shorter if need be.

As for the gearing, your idea of mountain drive and two speed rear sounds expensive. Two speed shifter, cable set plus mountain drive to get great range but crappy transitions. The 8 speed idea again is expensive. You have to have the rear triangle widened to fit the hub or you buy the whole kit from them with a new rear triangle.

Is it possible you just don't have the right Brompton? Could you sell the one you have and put the money towards a 6 speed and with -12% gearing? Someone else might appreciate what the original owner did for a light weight Brompton.

In the end it just sounds like a lot of work but maybe that is something that appeals to you.