I didn't actually go to check whether there is a working ticket office here or not. Anyway, in the separate building to the left of the main station building you will find the free toilets. Take a nose peg and paper with you or hold on for half a day. You will not be able to use the toilets on the train while in the station and the ones on the train will only be open for a very short time before you reach the Mongolian border town.
If you travel on the local train between Irkutsk and Ulan Bator, then you will spend around 4 hours here. After the document check you can leave the train and take a walk around.
I went to the local market which is rather small but within walking distance. There wasn't too much to buy there with your last roubles as there were mainly clothes but they also had bread, beer and sweets among the bits and pieces.
You will arrive in Naushki by train. If you travel on the local train between Irkutsk and Ulan Bator, then you will spend around 4 hours here. After the document check you can leave the train.
While you are waiting on the platform you may be surprised to see your train take off back into Russia. But don't worry they are only rearranging the train if it's the local one. Actually, when I travelled on it there were only two carriages going all the way from Irkutsk to Ulan Bator. The rest of them stayed in Naushki. Suddenly our carriages were back on track two.
A Mongolian woman from another compartment smuggled this little beauty into Mongolia. She shared the compartment with a Russian gold miner and I think the little doggy got some vodka for a quiet sleep tucked away.... He did pee on the train's blanket at some stage but the whole story was most entertaining!