What you're calling a tail battery is probably the tail motor. They burn out pretty quick on the cheaper helis with brushed motors.
If you are going to get into this hobby, then yes - you will need to get pretty good at soldering. If you need help there are some good how to solder vids on youtube.
Those little 3 channel helis are really just toy grade stuff - the controls don't even work the same as a hobby grade. They are a cheap way to get into the hobby, but I don't think they are worth the cost of repairing. My personal oppinion is now that you've tried it, step up to at least a 4 channel fixed pitch like one of the blade helicopters or even one of the 4 channel from wltoys. A little more difficult to fly, but much more fun once to get it under control. Parts are much easier to find and they're worth repairing while you learn the flying skills you'll need for a 6 channel collective pitch.