1. Why assembly is used?
Because there are certain things then can be done only in assembly and because assembly results in a faster code. For eg, "you can get access to unusual programming modes of your processor (e.g. 16 bit mode to interface startup, firmware, or legacy code on Intel PCs)". Read here for more reasons.
2. What assembly file are used?
From: https://www.kernel.org/doc/Documentation/arm/README
"The initial entry into the kernel is via head.S, which uses machine independent code. The machine is selected by the value of 'r1' on entry, which must be kept unique."
From https://www.ibm.com/developerworks/library/l-linuxboot/
"When the bzImage (for an i386 image) is invoked, you begin at ./arch/i386/boot/head.S in the start assembly routine (see Figure 3 for the major flow). This routine does some basic hardware setup and invokes the startup_32 routine in ./arch/i386/boot/compressed/head.S. This routine sets up a basic environment (stack, etc.) and clears the Block Started by Symbol (BSS). The kernel is then decompressed through a call to a C function called decompress_kernel (located in ./arch/i386/boot/compressed/misc.c). When the kernel is decompressed into memory, it is called. This is yet another startup_32 function, but this function is in ./arch/i386/kernel/head.S."
Apart from these assembly files, lot of linux kernel code has usage of inline assembly.
3. Architecture dependence?
And you are right about it being architecture dependent, that's why the linux kernel code is ported to different architecture.