Calculate the surface area of part B and the volume of concrete for part A.

The side length of the square is $2 \text{ m}$.

$$A_{square} = (2 \text{ m})^2 = 4 \text{ m}^2$$

The radius of each quarter circle is $1 \text{ m}$. Four quarter circles combine to form one full circle.

$$A_{circles} = \pi r^2 = \pi (1 \text{ m})^2 = \pi \text{ m}^2$$

Part B is the area of the square minus the area of the four quarter circles.

$$A_B = A_{square} - A_{circles} = 4 \text{ m}^2 - \pi \text{ m}^2 = (4 - \pi) \text{ m}^2$$

Using $\pi \approx 3.14159$:

$$A_B \approx (4 - 3.14159) \text{ m}^2 \approx 0.85841 \text{ m}^2$$

The surface area of part B is $\boxed{\text{}0.858 \text{ m}^2\text{}}$

b) The volume of concrete for part A

Part A consists of four quarter circles, which form one full circle with a radius of $1 \text{ m}$.

$$A_A = \pi r^2 = \pi (1 \text{ m})^2 = \pi \text{ m}^2$$

The height of part A is given as $45 \text{ cm}$.

$$h_A = 45 \text{ cm} = 0.45 \text{ m}$$

$$V_A = A_A \times h_A = \pi \text{ m}^2 \times 0.45 \text{ m} = 0.45 \pi \text{ m}^3$$

Using $\pi \approx 3.14159$:

$$V_A \approx 0.45 \times 3.14159 \text{ m}^3 \approx 1.41372 \text{ m}^3$$

The volume of concrete for part A is $\boxed{\text{}1.4137 \text{ m}^3\text{}}$

c) The volume of concrete for part B if its area is estimated at 1.2m²

The estimated area of part B is $1.2 \text{ m}^2$.
The height of part B is given as $20 \text{ cm}$. Convert this to meters:

$$h_B = 20 \text{ cm} = 0.20 \text{ m}$$

$$V_B = \text{Area of B} \times h_B = 1.2 \text{ m}^2 \times 0.20 \text{ m} = 0.24 \text{ m}^3$$

The volume of concrete for part B is $\boxed{\text{}0.24 \text{ m}^3\text{}}$