MIPS Relative Addressing
Addition sign is for relative addressing not concatenation.
$PC=$PC +I*4; means that program counter will point from itself by I*4 locations.

"What is maximum branch distance?" 
If we look beq or bne instruction, OP, RS, RT, OFFSET = 32bits. For offset is reserved 16bits so the maximum branch distance is 2^16=65535. Sometimes 2^16 is not enough to reach location jump and than you may use unconditional jump.

"What is the maximum offset from $s" I beleive the answer is the same 2^16.