You should have been given a companion as a gift from one of your previous objectives. If you already used it before that objective came up there is a companion available as a gift in the memory event going on now. It's a shiba inu available on completing the first board.

Why won't the objective that says, "Find an aging point when the horses wake up", give me my reward? I have refreshed the page and that didn't fix the problem.

Just a reminder, you should create your own topic in order to get an answer to your questions.

Make sure the horse has been put to bed and aged or you just aged your horse with an aging point and woke up fresh. It sounds like you found a horse that had found an aging point on a previous day and hadn't gone to bed. Also, remember your horse can not have a Morpheus Arms Black Market item equipped as Horses with that BMI will not find aging points when they wake up.