How to fix my designed calculator circuit using Logisim
You have a 4-bit full adder, so far OK. Then you connected a control input to the carry-in of the lowest bit. When you keep that control at 0 you still have your 4-bit adder. When you put it at 1 you will get the addition + 1, just as you described. Putting an inverter after the first output bit will 'solve' this ONLY for additions that had a 0 in the lowest bit (go figure out why).

If you want the control = 1 to give you the addition, and control = 0 must give 'something else, does not matter what' you could put the inverter in the control line.

BTW a 4-bit added will give you a 5-bit result. If you need an 8-bit 2s-complement result look up 'sign extension'. (This smells of homework, so I won't give away everything.)