read_character
LDR r0, =0xE000C014
LDRB r1, [r0]
BIC r1, r1, #0xFFFFFFF0
CMP r1, 0
BEQ read_character
LDR r6, =r1
LDR r2, [r6]
that BIC leaves bits 3:0 unchanged so if RDR, OE, PE or FE is set then read a character.
maybe instead do an AND or TST with 1 and compare if the RDR bit is set or not?
Likewise on the read the LSR and with 0x10 if set then send a character otherwise loop and try again? the code as you have written it will always set the 0x10 bit in r1, then shift it right 1 so that 0x08 is always set then compare with zero which should always fail since at least that one bit is always set, so are you seeing an infinite loop? with your tx code?