What will happen if we send the same coins? 
Because this transactions are not getting confirmed
Well this isn't actually very common. Unless you have a similar situation as I've had. Basically if two or more people are using the same address at the same time, there will be problems. Some transactions will result in being 'conflicted' and thus nothing really happens. This is rare though. Because this transactions are not getting confirmed My Bitcoin Core isn't synched to the network. Should I just not bother?
Without Core there isn't much that you can do. This really depends on how far behind you are. You could start syncing this very moment though.