Let's solve each of the expressions step by step:

1. Expression:

$3.5 \times \frac{6}{7} + \frac{5}{4} \times \frac{56}{21} + \frac{5}{7} - \frac{15}{35}$

Step-by-step:

• $3.5 \times \frac{6}{7} = 3$
• $\frac{5}{4} \times \frac{56}{21} = \frac{280}{84} = \frac{10}{3}$
• $\frac{5}{7} = \frac{5}{7}$
• $\frac{15}{35} = \frac{3}{7}$

Thus, the expression becomes: $3 + \frac{10}{3} + \frac{5}{7} - \frac{3}{7}$

Simplifying: $3 + \frac{10}{3} + \frac{2}{7}$

To add these, we need a common denominator for $3$, which is 21: $3 = \frac{63}{21}, \quad \frac{10}{3} = \frac{70}{21}, \quad \frac{2}{7} = \frac{6}{21}$

Adding them: $\frac{63 + 70 + 6}{21} = \frac{139}{21}$

So, the result is: $\boxed{\frac{139}{21}} \quad \text{or approximately } 6.62$

---

2. Expression:

$\left( \frac{22}{33} - \frac{19}{38} + \frac{14}{16} \right) \times \left( \frac{22}{33} + \frac{7}{28} \right)$

Step-by-step:

• $\frac{22}{33} = \frac{2}{3}$, and $\frac{14}{16} = \frac{7}{8}$
• So, the first part becomes: $\frac{2}{3} - \frac{19}{38} + \frac{7}{8}$ Finding a common denominator: $\frac{2}{3} = \frac{152}{228}, \quad \frac{19}{38} = \frac{114}{228}, \quad \frac{7}{8} = \frac{199.5}{228}$ So the expression becomes: $\frac{152-114+199.5}{228} = \frac{237.5}{228}$
• For the second part: $\frac{2}{3} + \frac{7}{28}$ Common denominator gives: $\frac{2}{3} = \frac{56}{84}, \quad \frac{7}{28} = \frac{21}{84}$ So, this becomes: $\frac{56+21}{84} = \frac{77}{84} = \frac{11}{12}$
• Now multiplying: $\frac{237.5}{228} \times \frac{11}{12} = \frac{237.5 \times 11}{228 \times 12}$

The result is: $\boxed{\frac{2612.5}{2736}} \quad \text{or approximately } 0.954$

---

3. Expression:

$\left( \frac{4}{3} + \frac{1}{5} \right) - \left( \frac{4}{15} \times \frac{5}{16} - \frac{4}{15} \times \frac{28}{5} \right) \times 0.6 + \frac{3}{5} \times 0.25$

Step-by-step:

• $\frac{4}{3} + \frac{1}{5} = \frac{20}{15} + \frac{3}{15} = \frac{23}{15}$
• $\frac{4}{15} \times \frac{5}{16} = \frac{20}{240} = \frac{1}{12}$
• $\frac{4}{15} \times \frac{28}{5} = \frac{112}{75}$

Now simplifying: [ \frac{1}{12} - \frac{112}{75} = \frac{25}{300} \text, which gives tan fold