You have used signed comparison operations, and on 32-bit registers.
This is ok, if the caller used the proper load instructions to fetch and convert the 8-bit/16-bit data from memory into registers that are being compared (or else otherwise managed the conversion from 8-bit/16-bit to 32-bit).
For the unsigned 8-bit code you would need to use LDRB and for signed 16-bit, LDRSH.
In the unsigned case, using LDRB will convert 8-bit unsigned data loaded from memory to 32-bit by zero extension — the top 24 bits of the register get zero, and the lower order 8 bits the value from memory. This final value in the register after LDRB is always going to be >= 0 whether interpreted as signed or unsigned in 32-bits, since the sign bit in the registers will be zeros. It is up to you whether to consider the 32-bit value signed or unsigned, because we know that it will always be positive (non-negative) so in a sense it doesn’t matter. The C language would say it is int which is a signed data type, because it gravitates toward int and int can easily hold any value from a signed byte and/or an unsigned byte.
In the signed case, using LDRSH will convert 16-bit signed data loaded from memory to 32-bit signed value in the register. It does this by propagating the sign bit from bit 15 of the 16-bit memory halfword into all the bits of the upper half of the register. It is important in this case to consider the 32-bit register with the signed data type, since we may have negative or positive values.
When you have 32-bit values in memory, they can neither be sign extended nor zero extended to fit in a 32-bit register, as all the bits are already specified from memory. As a result, for unsigned you would have to use unsigned >= conditions — meaning the branch instruction would have to change to BHS (branch higher or same), whereas for signed you would have to use signed >= conditions (BGE).1
Because your code is said to use smaller data types (smaller than 32-bits: 8-bit unsigned, and 16-bit signed) you can get away with using signed comparison for both types — provided the values are properly and accordingly extended to 32-bits into the registers.
If the values were loaded from memory into registers with an incorrect sign/zero extension, you would have to fix that with other instructions before using the comparison operations. On x86, however, you can compare just the lower 8-bits or just the lower 16-bits of the registers with each other due to its partial register feature. On the x86 processor using smaller size compares, the above comments about the full 32-bit value made above1 would also apply.