Have it tested and also have your alternator tested.
Yes, the battery can be replaced. There are a number of YouTube videos available outlining the exact steps; however, keep in mind that doing so may void your warranty.
Batteries should be replaced about every 3 to 5 years, some can even last seven. However, it is obvious that if the battery dies (with no ability to "jump"), is corroted, or gets a dead cell in it then it should be replaced.
You cannot reset the odometer in your car, however you can reset your trip odometer.
When you hear a clicking noise is most likely a battery problem however you stated that the battery was replaced so i suggest you check the condition of your cables look for rust or corrosion etc.
Not likely but as alterantor keeps trying to charge a weak battery it may wear out, however as you are not likely to keep a bad battery in the car for so long there should be no damage to alternator if battery is replaced.
This may be a sign that your battery needs to be replaced. However, there may be other causes as well.
According to Apple, you should be able to get around 1000 battery cycles out of your Macbook Pro before the battery will need to be replaced. This comes down to 5 years of normal battery usage. However, over time, the battery's capacity will significantly diminish.
The odometer is electronic, there is a plug in on the back of the speedometer, however the plugin for the odometer also may power other controls, so this may not be a good idea. I dont know why your trying to stop the odometer but your out of luck the computer keeps track of your information your odometer is just a read out like a monitor
First, why was the battery replaced? If there was a pre-existing problem (like a bad starter, for example), replacing the battery will not solve the problem. If, however, the car started fine before battery replacement, then the problem could be that the battery terminals (clamps) were not sufficiently tightened. Don't laugh, but there have been instances where the plastic cap(s) covering the new battery's positive and negative terminals were not removed (duh!). Remove those plastic caps.
The life of a car battery really depends on many factors, in addition to time. Amount of use and climate are key factors in the life of a battery. One can expect to have to replace a battery generally every 3 or 4 years, however.
It normally leads straight down to the starter. However, I have seen some that lead into a smaller wire, going right to the battery. It all depends on if the wiring has been messed with previously on your car, or if a battery cable has been replaced.
A battery is only an electrical storage device. If the battery is faulty it will not be able to store electrical energy. On the other hand, if the battery is ok, it could be discharged because the alternator cannot create sufficient energy to keep the battery charged. If you are able to charge the battery the problem is in the alternator or an electrical connection. If you can't charge the battery, go ahead and change it. However, replacing a good battery will only make the vehicle run briefly. If the charging system isn't working a new battery won't solve the problem.