If you don't have FPGA experience in house, it can be quite a significant cost to build it up / learning curve.
In broad strokes, what you're describing (your background, what you are doing) might be a good fit for OpenCL.
https://www.altera.com/products/design-software/embedded-software-developers/opencl/overview.html And your development might go like: cleanup Matlab and translate to OpenCL entirely on PC, figure out what OpenCL functions you want pushed into the FPGA vs. kept in software on the ARM side of your SoC.
In general for some of your questions:
a) yes, using a SoC with hard ARM with Linux will absolutely make your life easier especially if you are coming from software background.
b) anything which is non-realtime related, think about doing it in software and not FPGA. if you aren't doing (continuous) Video processing and are instead only doing (single frame) Image processing, you can limit yourself to just creating "accelerator" IP blocks in the FPGA side of an SoC, where software drives the algorithm and does all the I/O and can easily fill in missing functionality that is outside your reach to develop the FPGA version of. Continuous real-time processing of video, you may need to do all of it in the FPGA with software limited to control activity.
c) video in / video out if not on your development kit can often be added with a daughter card. Terasic is one vendor (
http://www.terasic.com.tw/cgi-bin/page/archive.pl?language=english&categoryno=65#category68). Sometimes pairing daughter cards with a compatible development kit can be challenging, so before you buy, contact them.
You've been mentioning SoC, but also mentioned you have DE0-NANO which isn't an SoC (Cyclone IV, 22KLE, no ARM). There is also the DE0-NANO-SOC aka Atlas-SoC (Cylclone V SoC, Ethernet, etc.).
Getting started with a Cyclone IV, I'd recommend doing all your software / I/O on the PC and communicate with your hardware over JTAG using System Console.
Getting started with a Cyclone V SoC, you can just get Linux up and running and communicate with your hardware directly on your board.