how long should I charge my new Aspire E-15 574G for initially?

If you want that your notebook battery has a great performance, the first thing to be done by the first charge 100% the calibration. Calibration of the battery levels the load of each cell that may eventually uneven plant. Never leave your battery reaches 0% of charge, because this habit, and dramatically decrease battery life of your notebook, subject to the risk of unusable her to leave her without charge for a while. The only exception is when you need to perform calibrations.

And day by day, how many hours should I leave carrying?

One should not think of the "number of hours", but in "load percentage." You can leave the battery to reach 100% charge usually to keep connected to outlet, it will "pause" the load going to use only the energy source. Identify this behavior through the charge indicator LEDs on your notebook. Remembering: It is recommended that you leave your battery runs with load below 20% or charge it to 100% often. When you charge your battery up to the limit, it will warm up and it is harmful. If you choose to use the notebook without the battery, direct at source, charge the battery to 60% charge and store it in a cool, dry place. But do not get more than 15 days without using it . I have helped