### Problem 1 Calculation:

Given: $(1)(-10)+(-7)-(+3)+(+2)$

Step-by-step calculation:

1. Simplify the expression by following the order of operations:
$$= (-10) + (-7) - (+3) + (+2)$$
2. Combine like terms:
$$= -10 - 7 - 3 + 2$$
3. Continue simplification:
$$= -18$$
Final Answer:
$$\boxed{-18}$$

### Problem 2 Calculation:

Given: $(-2)^{3}\div 4-(-1)^{2023}+|-6|\times (-1)$

Step-by-step calculation:

1. Evaluate each part of the expression:
$$= (-8) \div 4 + 1 + 6 \times (-1)$$
2. Perform the division and multiplication:
$$= -2 + 1 - 6$$
3. Combine the results:
$$= -7$$
Final Answer:
$$\boxed{-7}$$

### Problem 3 Calculation:

Given: $(\frac{1}{3}-\frac{1}{4}+\frac{5}{6})\times(-24)$

Step-by-step calculation:

1. Distribute $-24$ across the fractions:
$$= -24 \times \frac{1}{3} + 24 \times \frac{1}{4} - 24 \times \frac{5}{6}$$
2. Perform the multiplication for each term:
$$= -8 + 6 - 20$$
3. Combine the results:
$$= -22$$
Final Answer:
$$\boxed{-22}$$