Sometimes it is necessary to use so-called measure words or classifiers. For example, in English we do not say ‘buy two breads’ or ‘bring five shoes’. Instead the correct phrases are ‘buy two loaves of bread’ and ‘bring five pairs of shoes’. In these examples the articles loaves and pairs are the measure words which cannot be omitted. In some other languages, like Vietamese or Chinese, the use of classifiers is more frequent and strict. For more information please read https://en.wikipedia.org/wiki/Chinese_classifier, https://en.wikipedia.org/wiki/Vietnamese_grammar#Classifier_position.

Q1. By analyzing the given six sentences we can guess that the word cái is a classifier (it occurs too many times, so it should be an article) and the expression cái này là should stand for ‘this is’. Similarly one could say: This pair is a beautiful pair of shoes. But in English we would omit the first 'pair' and use just 'this is'. If we accept this assumption then it is not hard to match the given sentences and translations:

1. Cái này là cái hoa.
This is a flower.

2. Mình mua ba cái hoa.
I buy three flowers.

3. Bác bán cái đĩa kia.
Uncle sells that plate.

4. Cái bình này đẹp.
This vase is beautiful.

5. Cái này là cái bình đẹp.
This is a beautiful vase.

6. Mình đem năm cái đĩa.
I bring five plates.

Q2. For the second question the translations are the following:

This is a beautiful flower.
Cái này là cái hoa đẹp.

I sell five beautiful flowers.
Mình bán năm cái hoa đẹp.

This is a plate.
Cái này là cái đĩa.