Dell Inspiron 1501 Battery Not Detected

A battery can only be charged and discharged so many times and Li batteries are better maintained when kept at or near full charge. The life of the battery depends on how many times and how deeply the battery has been discharged.

If this is the original battery I would say it's time for a new one.

I don't know what you are calling MHZ. There is no such specification for a battery. Maybe you mean mAh which is milli-Amp-hours which is a measure of how much power the battery will hold. If you plan on using it on battery power for long periods then you need higher mAh. If you will use it mostly from the wall outlet and only occasionally from the battery pack, you can buy a cheaper battery with lower mAh. In general, the less you use the battery (charge and discharge it) the longer it will last regardless of the mAh rating. So use it powered froma wall outlet as often as possible.

The primary consideration is that it will physically fit the battery bay in the computer and the connector inside that battery bay. As long as that is correct and the manufacturer says it will fit the Inspiron 1501 you won't neded a different AC adapter. A larger mAh may take longer to fully charge but the battery chemistry controls how fast it can be charged. Using a different AC adapter with a different charge rate can damage the battery and possibly cause overheating and a fire. So stick with the charger you have as long as it is working. If the charger ever quits working make sure any replacement you get has exactly the same specifications as shown on the label on the charger.