I'm afraid not, there is no floppy drive to SATA connector. I don't think the SATA port would know what to do with the floppy drive, it was never designed to talk to it.
For MS Office, email and internet only kinda work, I would go with the AMD.
Either one will be more then enough power, but you will save money on the AMD, and the built in GPU is just nice to have for the savings.
You will need the make and model of your laptop to determine if there are Win 7 drivers/software available, there should be.
You will also need to purchase a retail copy of Windows 7, as the Home version of 8 does not support downgrade rights.
I'm not sure what the ultimate solution would be. But I would be careful with your idea of pushing warmer air into the case, you don't want to cause condensation.
In this case, I would actually go with the monitor. Yours runs at 1280x1024, not a hard resolution for newer graphics cards. You won't see a huge jump in performance with a more expensive GPU.
128c is way too high of a temp, that's why you are shutting down. Check to make sure you installed that heatsink correctly. It has a proper amount of thermal paste, and is pressed tighly against the CPU.