Is it possible to fill in a very small gap between front tooth (#9) and side tooth (#10)?

Just making sure you have your teeth numbers correct, #8 and #9 are the front two incisors, central incisors.  Teeth number #7 and #10 are the ones next to the front two teeth, and they are the lateral incisors.  All of the incisors, #7,8,9,10 are considered front teeth and can have the gaps closed with direct composite bonding.The canines, #6 and #11 can be bonded to close the gaps if the space isn't too large.Usually direct composite bonding is not done on the bicuspids to fill gaps. Sometimes 2 or 3 surface fillings will close small gaps, but because there is so much force when biting with those teeth, fillings to close the gaps on those teeth don't hold up as well as onlays, veneers or crowns.

Absolutely.  Direct composite bonding is ideal for small spaces between any of the front six teeth either on the upper or lower arches.

Yes, we do it anywhere in the mouth. Whether or not it can be done in your particular case is up to your dentist. Sometimes a limited short term orthodontic treatment is a better choice.