TerASIC DE2-115 and Custom FPGA Component

The answer to all your questions is mostly: you need to create a new SOPC component.

There are however, a few different ways to go about it.

a) make your component just an Avalon-MM slave and put the memory in your component (FPGA internal memory). You expose that memory block to the processor, plus whatever configuration register you need, through the slave interface

b) make your component an Avalon-MM master, which writes to another Avalon-MM memory slave component (FPGA internal RAM, board SRAM, board DRAM).

Most likely, it will also need an Avalon-MM slave interface for configuration (ie, which memory address will it write to)

c) make our component an Avalon-ST source and use a SGDMA component to write to another Avalon-MM memory slave (FPGA internal RAM, board SRAM, board DRAM).

"a" or "c" are probably the best, depending on your needs

For the interrupt, same thing: your component needs to have an Avalon Interrupt interface as well.

You probably need to skim through the Avalon and SOPC documentation.