Good job removing the battery! I replaced mine with a rechargable cordless phone battery (confirm polarity first).
The The flickerfixer output should be able to go into the input port on the Picasso II with the proper cable. This way the Picasso will pass thru native Amiga screen modes AND output it's own resolutions. No monitor cable swapping required. Have you done this?
A longer SCSI cable and SCSI CDrom should be all that's required (no drivers, this is an Amiga). You will have to set unique SCSI ID numbers (0 thru 6) for all devices connected. If the CDrom is the last internal SCSI device on the ribbon cable, I think it will need termination. All other internal devices should have termination turn OFF. This termination scheme will be true of any external devices as well.
You could try for a SCSI CDwriter as well, these turn up on e-Bay from time2time.
Your machine has much potential added to it already. A minority of us try to use Amigas for as much as possible, like surfing, Mp3s, graphics, office, faxing, etc. This post came from an Amiga.
It would help others help you if you give more information, like motherboard revision, rom rev on the GVP SCSI controller, fast ram available, etc.