The injured toddler should go to see a dentist immediately so that the dentist could conduct a thorough examination and follow up for the tooth subsequent.
For more information, please refer to "Traumatic Injury to Oral Structure and Teeth" of "Oral Problems".
It depends on the severity of the fracture to determine whether it is going to affect your child's speech. It will not affect his development of speech if the fracture is minor. If the fracture is rather large then it might affect his articulation. You need to bring your child to the dentist to have the situation evaluated.
There are many reasons for tooth sensitivity when drinking cold beverages, such as dental caries, periodontal disease, sensitivity because of exposed root, tooth fracture, and so on. To understand your current situation, you should go to a dentist for a dental check-up. For more information, please refer to "Sensitive teeth" and "Toothache and painful gingivae (gums)" of "Oral Problem".
For information about tooth discolouration , please refer to "Discoloration of teeth" of "Oral Problems".