Yes, you can put only garden waste in the Patta Kambha. The garden waste will compost slowly if you do not add any kitchen waste to it. But it will eventually compost.
Adding accelerator helps but is not critical. You can use the Daily Dump accelerator or use any other that you know about. Semi-composted materialalso is a good accelerator.
You should then use two Patta Kambhas and alternate dumping. This will distribute the waste evenly and save you the bother of interchanging units too often. Add water regularly - this will help reduce volume of garden waste fast.
The waste on the sides tends to be dry because of absorption of moisture by the terracotta walls. This needs to be combined with the wet waste in the center. Use your tools or your hands (in gloves) to stir and combine the dried edges with the wet center.
The main difference is that one is modular and easy to empty out eventually while the other is very like a pit - you keep filling and once in 6 months you harvest the compost.
Yes, if you do not add water - then the dried leaves do not compost for a very very long time and your Patta Kambha acts as a store - very much like a grainary. This store is useful if you have another Daily Dump composter like the Mota Lota, Kambha or Gamla. These products need dried leaves added to the kitchen waste. Some customers install a Patta Kambha next to a kitchen composter for this reason.
No problem, the compost enjoys the break! Just check moisture levels when you get back and stir the pile.