What are these connectors called?

[guerney]

...also, are they easy to solder? Photo:

 

[Nealh]

Bullet crimp connectors likely about 4 or 5mm.
Personally one is better off soldering direct or using a better quality connector like an XT, Powerepole (Anderson) or Deans.

 

[guerney]

Would these be ok connecting to the battery?

400PCS MOTORCYCLE WIRING 3.9MM HARNESS LOOM BRASS BULLET CONNECTORS ELECTRICAL | eBay

400PCS Wire Connectors. 3.9mm Female Bullet Connectors--50Pcs. 3.9mm Male Bullet Connectors--50Pcs. US-Wire Connectors. UK-Wire Connectors. Material: Brass, Tin. Suitable for motorcycle, scooter, car, truck, quad bike, trike, etc.

www.ebay.co.uk

 

[Nealh]

Only if you can't solder, use the brass/copper bullets. The weak point is the insulation, heat can melt it overtime and this is where any frying will take play as they short. Use heat shrink over the wire joint and then the insuation sleeve.
Copper or gold soldered connectors with decent insulation separation are best.