I understand every bit of the C compilation process (how the object files are linked to create the executable). But about the loader itself (which starts the program running) I have a few doubts.
Is the loader part of the kernel?
How exactly is the ./firefox or some command like that loaded? I mean you normally type such commands into the terminal which loads the executable I presume. So is the loader a component of the shell?
I think I'm also confused about where the terminal/shell fits into all of this and what its role is.
The format of an executable determines how it will be loaded. For example executables with "#!" as the first two characters are loaded by the kernel by executing the named interpreter and feeding the file to it as the first argument. If the executable is formatted as a PE, ELF, or MachO binary then the kernel uses an intrepter for that format that is built in to the kernel in order to find the executable code and data and then choose the next step.
In the case of a dynamically linked ELF, the next step is to execute the dynamic loader (usually ld.so) in order to find the libraries, load them, abd resolve the symbols. This all happens in userspace. The kernel is more or less unaware of dynamic linking, because it all happens in userspace after the kernel has handed control to the interprter named in the ELF file.