Convert the weight of tomatoes from a mixed fraction to an improper fraction.

$$
2\frac{1}{2} \text{ kg} = \frac{(2 \times 2) + 1}{2} \text{ kg} = \frac{5}{2} \text{ kg}
$$

$$
\text{Weight of onions} = 3 \times \frac{5}{2} \text{ kg} = \frac{15}{2} \text{ kg}
$$
$$
\text{Weight of onions} = 7.5 \text{ kg}
$$
The weight of onions is $\boxed{\text{7.5 kg}}$.

$$
\text{Sweets eaten} = \frac{7}{10} \times 30
$$
$$
\text{Sweets eaten} = 7 \times \frac{30}{10}
$$
$$
\text{Sweets eaten} = 7 \times 3
$$
$$
\text{Sweets eaten} = 21
$$
Harish ate $\boxed{\text{21 pieces}}$ of sweets.

$$
\text{Number of boys} = \frac{1}{3} \times 480
$$
$$
\text{Number of boys} = \frac{480}{3}
$$
$$
\text{Number of boys} = 160
$$
The number of boys is $\boxed{\text{160}}$.

$$
\text{Distance by bus} = \frac{3}{5} \times 5 \text{ km}
$$
$$
\text{Distance by bus} = 3 \text{ km}
$$
The student travels $\boxed{\text{3 km}}$ by bus.

$$
15\frac{1}{5} \text{ m} = \frac{(15 \times 5) + 1}{5} \text{ m} = \frac{75 + 1}{5} \text{ m} = \frac{76}{5} \text{ m}
$$

$$
\text{Length of each piece} = \frac{76}{5} \text{ m} \div 12
$$
$$
\text{Length of each piece} = \frac{76}{5} \times \frac{1}{12} \text{ m}
$$
$$
\text{Length of each piece} = \frac{76}{60} \text{ m}
$$

$$
\text{Length of each piece} = \frac{76 \div 4}{60 \div 4} \text{ m} = \frac{19}{15} \text{ m}
$$
$$
\text{Length of each piece} = 1\frac{4}{15} \text{ m}
$$
The length of each piece is $\boxed{\frac{19}{15} \text{ m}}$ or $\boxed{1\frac{4}{15} \text{ m}}$.