Are there 8 bit ARM processors?
Assuming "n bit" refers to the size of the general purpose registers all arm processors are 32 or 64 bit.

Prior to designing the ARM processor Acorn's computers had been designed around the mos technology 6502 and variants. They decided to leapfrog over the 16 bit generation and go straight to a 32-bit design. Instructions were 32 bits wide and so was the data path. Initially some bits were used as flag bits limiting addreses to 26-bit but these flags were later done away with allowing a fully 32-bit address space.

Acorn computers failed to maintain a viable position in the market but before that happened ARM had been spun off into a seperate company. ARM was a low power architecture and started to see a lot of use in mobile/embedded computing. Eventually as transistors got cheaper (in both cost and power terms) it worked it's way down into the microcontroller market.

Arm later introduced a mode called "Thumb" (sometimes reffered to as "Thumb1") where the instructions were only 16 bits wide. The registers however remained 32 bit. Thumb in it's original form was an incomplete instruction set, certain important operations could only be performed by switching back to Arm mode.

Even more recently arm introduced "Thumb2". This extended Thumb to produce a complete instruction set using a mixture of 16-bit and 32-bit instructions. Again the data registeres remained 32-bit. Modern ARM microcontrollers only support Thumb2 mode (sometimes with only a subset of the full "thumb2" instruction set), not traditional arm mode.