Can you catch HIV from an HIV positive teething baby who sucks and chews on your finger?

Yes. It is certainly possible. If there is a break in the skin, yes.
Unlikely. For the same reason that cunnilingus does not appear to transmit hiv. Salivary enzymes tend to inactivate the virus. Unless baby is bleeding and causes breaks in your skin it would be virtually reportable for you to get HIV infection in this manner.