Do babies only sits up from tummy position when they start crawling? If not when will they start doing that? In addition, will propping up a cushion below the tummy helps them to crawl ?

They will learn to crawl and sit up when they are developmentally ready. Give your child a lot of free time on the play mat and use toys to attract her for movement. This is on of my favourite article on why we need to give our babies freedom to move and give them time to be ready to crawl and sit. http://www.janetlansbury.com/2012/04/sitting-babies-up-the-downside/