By definition, you can't convert between proper and improper fractions. You can convert improper fractions to mixed fractions, and vice versa.
Convert the mixed fractions into improper fractions. Convert the integer into a fraction by simply dividing it by 1
convert into a mixed number.
Convert them to improper fractions and proceed.
You can't. Improper and proper fractions are two different things. You can convert an improper fraction to a mixed number.
The easiest is to convert both mixed form numbers to improper fractions, do the subtraction (as normal1) and if the result is an improper fraction convert it to mixed form. 1 by converting the improper fractions to equivalent [improper] fractions with a common denominator and subtracting the resultant numerators.
You cannot. They are two disjoint subsets of rational numbers.
Convert any mixed numbers to improper fractions. Once you have a fraction (proper or improper) do the division. 2/4 = 2 divided by 4 = 0.5
Convert them to improper fractions and proceed.
It is best to convert the mixed fraction to an improper fraction. They are then added together in the same way as proper fractions are added together.
Convert them to improper fractions and proceed. The answer will be positive.
To find a volume you usually need to multiply values together. When working with mixed numbers it is usually easier to convert them into improper fractions, do the calculations and convert any resulting improper fraction into a mixed number. So you don't need to use either format, it's just that improper fractions are easier to manipulate.