If the given interchanges namely: signs $+$ and $÷$ and numbers $6$ and $3$ are made in signs and numbers, which one of the following four equations would be correct?

Let's apply the interchanges ($+⟷÷$ and $6⟷3$) to each option and verify them using BODMAS rules:
* Checking Option A: $6+3÷3=3$
After interchanging, it becomes:

$$3÷6+6$$

Using BODMAS: $\frac{3}{6}+6=0.5+6=6.5\ne 3$ (Incorrect)
* Checking Option B: $3÷6+2=5$
After interchanging, it becomes:

$$6+3÷2$$

Using BODMAS: $6+\frac{3}{2}=6+1.5=7.5\ne 5$ (Incorrect)
* Checking Option C: $3+6÷4=6$
After interchanging, it becomes:

$$6÷3+4=6$$

Using BODMAS:

$$\text{LHS}=(6÷3)+4=2+4=6$$

$$\text{RHS}=6$$

Since $\text{LHS}=\text{RHS}$, Option C is correct.
* Checking Option D: $6+3÷5=7$
After interchanging, it becomes:

$$3÷6+5$$

Using BODMAS: $\frac{3}{6}+5=0.5+5=5.5\ne 7$ (Incorrect)