1. What is the difference between a rate and a ratio?

rate is a comparison of kinds of quantities measured in different units.

e.g. km / hr

ratio compares the kinds of quantities measured in the same units.

e.g. In baking: 300g of flour to every 100g of butter.

2. Should ratios always be written in their simplest form?

Usually ratios should be written in their simplest form although sometimes it may be clearer to understand a problem if they are kept in some other form.