The short answer is yes, it is best to play Challenges in order. The daily Quests often build upon each other and skipping ahead can cause you to miss important information.
In Squad Play there is a day counter on the bottom of the Squad Play tab in your app. Each Squad Challenge is 5 days and there is a circle with the number for each day. Days you have completed will be fully shaded blue. The current day will have a blue border. If you miss a day, simply click the day number you missed and go back to catch up.
In Solo Play mode, complete the Quests in order from top to bottom. You can activate Power-ups in any order, as well as Bad Guys. Sometimes Bad Guys build upon learning in Quests, so if you jump ahead you may miss some foundational information but you can Battle the Bad Guy anyway. If you find one of these Bad Guys, consider not vanquishing it so you can battle it again after you complete the related Quest.