I have generally seen very little crossover between the PIC and Arduino/AVR communities...
There is definitely a library that supports SD cards on PIC devices (use whatever resources you use for finding info on PICs - I'd just be googling) - using SD cards is such a common task, it's inconceivable that there would not be.
An arduino ethernet shield - I'm not so optimistic about; it's unusual to see shields used with non-arduino hardware. Why not just use something like an ESP8266 to get WiFi? Those are cheaper than dirt, and as a result everyone and their mom is using them, both as standalone microcontrollers and low cost WiFi adapters. There's sure to be resources for using them with PIC.
Ooohh, ugh - yeah, wired solutions are more expensive now, and not as well supported, by a good margin. Somehow I thought you were talking about the WiFi shield. Everyone wants wifi now.
I'm sure there are ethernet adapters that people use with PICs for which libraries exist. Take a look around on PIC forums.
I am doing this with ethrnet2 library.
When finished I will update this post.
From what I see in the library, the thing that has to be done is to change the SPI related functions in utility/W5500.cpp file, so they work with the PIC SPI hardware or software one.
And a little message to DrAzzy:
PIC and AVR are now under the same family of Microchip. Dividing to different communities when we talk about hardware is a little bit like diving people to which soccer team they support. I never found an order not to use arduino shield with other microcontrollers different than AVRs. It is just a matter of know-how to do it.