Travelling overseas with MacBook Pro

Hey guys,

Thank you in advance. I recently moved from Canada to India but forgot to buy a travel adapter due to different type of charging prongs. Apple Store is pretty far from my town and it takes atleast 14 days for getting the travel adapter online. So, I plugged the Mac with a plug. Could you help with following questions:

1. Do I need a conversion plug to change anything in terms of voltage or anything? (My guess is no since the adapter would do that but still confirming).
2. Does using any plug and not the Apple issued travel adapter make any difference. Would it mess with battery or anything?
3. The plug is charging my Mac real slow. Could it be because of the plug that I’m using for adapter?

Including the picture as well

Thanks