As to thickness of wire and cell...I recently bought some 4S packs that came with 8AWG wire on them....I was like..."you have to be kidding me!!!"...but they are 45C batteries...
And....hopefully the soldering iron you bought has a "chisel" tip, and not a "pencil" tip. A pencil tip is fine for soldering small electronics stuff, but not for soldering batteries. The iron I use most often is the
Weller SP40L, which is a 40 watt iron, and will solder even 8AWG wire. The only bad thing about this iron, is that it seems to go through tips fairly often, but they are replaceable, and are not too expensive.. Both the irons and the tips are available at any Ace Hardware, and lots of hobby shops.
You should also purchase a soldering iron "tip cleaner" these are made of synthetic sponge, and you put water into them, or are made of metal strands (Google them)...
SteveT