You're on the right track. The balancer will connect to your charger's outputs where it says charger on the balancer. Then the lipo will connect to the balancer thru both sets of wires. This is a charge thru type setup which is what I assume I'm looking at since balancer shows place for the charger output.

The small 4 wire connector is the balance connector and it will go to the balancer. Balancer uses it to read voltages from the cells and adjust them to balance. The balancer will also connect to the lipos main power leads and charge them them while balancing.

Charge rate ideally is 5.4amps or as close to it as your charge will allow, say 5amps. You don't want to go higher - the the 1C rate is 5400/1000. They mean charge as a 2S - the lipo 'pieces' are wired together in parallel so they are a 2S lipo (actually a 2S2P). Your charger must have a lipo charging selection - do not attempt to charge the lipo as anything other than a lipo - thats unsafe.

As far as hooking it all together, you need compatible ends dictated by whats on the lipo. I can't see whats on the end of the main power leads, but you need to match that with the lead from balancer to lipo (opposite end obviously). I know Thunderpower uses a TP/FP style balance lead - you'll have to have the matching end on the balance cable from the balancer. Its not that hard give compatible connections on all leads. I'm not familar with that balancer, but I'm going to guess you'll need adapters for it to work with the TP lipo you've got.