I don't know personally, I'm just going from the scriptures. According to the scriptures, yes, you can be reborn as an animal. From the Kamma Sutta, those who harm other living beings physically may get the Kamma of being reborn sickly. There is a teaching that those who are given to violence and kill living beings, if they are reborn human, will have a short life. Those that harm others physically could be reborn sickly or not physically endowed perfectly. Those who are generous, if they are reborn human, could be reborn rich. Those who are not given to anger, are compassionate toward living beings, even when much is said, if they are reborn human, are reborn beautiful.
So if we look within our own experience, sometimes if we are generous, we feel as if we have abundance, and we are reborn rich at that moment. If we are angry, even if we are normally beautiful, we become ugly.
As to handicapped people, it would appear that mentally or physically handicapped people have some Kamma to work out.