How much power your laptop is using normally
A slight buzzing sound that varies with current draw (how much power your computer is using) is normal. Also heat is a natural byproduct of its operation. They can even get almost too hot to touch when under high loads.It shouldn't be anything to worry about.
I personally leave my laptop battery in my laptop at all times, as it acts as an uninterruptible power supply if the power goes out for any reason. It has saved me a few times.Taking out your battery will extend its useful life. But lithium batteries degrade over time anyway, and it will not save your work in the event of a power outage – so in my opinion, it's not worth taking it out.
It's the heat that speeds up the degradation of your battery. Once the battery reaches full charge, it completely stops charging (for all intents and purposes). It it still not worth taking the battery out for the reason I mentioned above.
For storage, keep it at 40% (check it once in a while to make sure it hasn't dropped, do not ever let it completely discharge it may degrade 20% or more in an instant)
The first Dell notebook AC Adatper I had with this laptop has some kind of degraded wire, it has to be curled in a certain way or it continually beeps with no green LED and doesn't supply power. I keep this one at home where it doesn't need to be moved. New properly working ones haven't beeped at all, so maybe ask Dell about that.And it does get hot, it's a 90W adapter and draw goes above 70W during games.
I would leave battery out but the AC cord falls out far too easily. Even being in 100% of the time it's only degraded 50% in 2+ years according to RMClock. Not too bad, still manages >1.5 hrs light use (6cell 56Wh battery in a Vostro 1500).
Any question about the battey knowledge you can go to USA online store www.battery-replacement.org and the UK online stores www.battery-stores.co.uk check it.