iPad Air 3 and Apple Pencil 1 care.

Charging your Apple Pencil directly from your iPad will cause no issues or damage to your iPad - in fact, your Pencil will be optimally charged when charging directly from the iPad.

You should, however, be mindful that the Pencil or iPad can be physically damaged while the Pencil is connected to the iPad. Stress placed on the Lightning connection can damage either the iPad Lightning port - or the Lightning plug of the Pencil. As such, it may be prudent to only charge the Pencil from the iPad when both a lying flat on a tabletop - undisturbed.

As an alternative, you can use the inline adapter that was supplied in the box with your Pencil - and use this to connect the Pencil to your iPad Power Adapter. Changing will be slower than when charging from the iPad, but their is much less likelihood of causing connector damage.

You may fund this support page to be helpful with pairing, charging and use of the Pencil with your iPad:

Connect Apple Pencil with your iPad - Apple Support

No.

No damage will be caused.

A small, seperate power block plug-in charge adapter should hsvr been included in the box with your Pencil 1st generation for charging the Pencil without needing the iPad all the time.

You need to maintain some percentage of charge level in the Pencil, AT ALL TIMES!

The inline adapter was included in the box in which your Apple Pencil was purchased - along with a spare Pencil Tip.

Spare inline adapters are not available for purchase from Apple. However, if you visit your local Apple store and ask very nicely, they may be able to help. Otherwise, third-party alternatives are readily available from Amazon or eBay.

You didn't get an adapter inside of your Pencil box when you purchased?

It should have come with a seperate charging adapter inside the box.

How long has it been since you purchased this Pencil and did you start using this Pencil right away or did it sit unused for a prolonged period of time?