Is it obligatory to wait for the Imam to straighten up from rukūʿ before straightening up, and does the same ruling apply to rising from sujud and the tashahhud?

It is better for the ma'mum (follower in prayer) to delay his actions in prayer behind the imam (prayer leader), so he does not equal him or precede him. This is because it is mustahabb (recommended) for the ma'mum to begin his actions in prayer after the imam has finished his. Doing an action simultaneously with the imam is makruh (disliked) according to most scholars. However, if one performs an action at the same time as his imam, his prayer is valid, though it involves an imperfection.