Can I buy a pair of shoes on sale during Chol Hamoed and then wear them? Can I buy new clothing or a new hairbrush and wear or use them during Chol Hamoed? Can I buy a blush brush for make-up and use this for the rest of the Chag?

In general, buying shoes, clothes or hair brushes on Chol Hamoed is not the right thing to do; these things should be bought before or after Chag. If you need the item for the Chag or it will be more expensive after the Chag, you may buy it during Chol Hamoed. (Shmirat Shabbat Kehichata 67, 22-30)