The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.x
Apple ended major update support for these models of iPad in September 2019 - although they have since received occasional “point” security updates, the most recent being released January 2023. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU capabilities and available RAM) for newer versions of iOS/iPadOS.
Many App developers have dropped support for iOS versions preceding iOS versions for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS) making their currently available Apps incompatible with earlier versions.
Whilst some App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports newer versions of iPadOS.
For information, here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:
32-bit devices (obsolete)
iPad1 - iOS 5.1.1
iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi+Cellular)
iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi+Cellular)
64-bit devices
iPad Air1*, iPad mini2 and iPad mini3* - iOS 12.5.7
iPad Air2, iPad mini4 - iPadOS 15.8.3
iPad5, iPad Pro (9.7"/12.9" 1st generation) - iPadOS 16.7.10
iPad6, iPad Pro (10.5"/12.9" 2nd generation) - iPadOS 17.7
(*) obsolete
Newer models are all able to be updated to the current version - iPadOS 18.0.1 (17.7 optional)
- iPad Pro 13" (M4)
- iPad Pro 12.9" (3rd generation and later)
- iPad Pro 11" (1st generation and later + M4)
- iPad Air (3rd generation and later + M2)
- iPad (7th generation and later)
- iPad mini (5th generation and later)
As for a third-party "Pencil", you have very little choice. Your iPad fundamentally does not support Apple Pencil. Third-party alternatives that use Bluetooth, are entirely reliant upon support for the specific Bluetooth stylus being supplied by individual Apps - and as such, this limitation fundamentally restricts usefulness.
The remaining option is to use a basic capacitive stylus. This type of stylus is totally passive - and has no more functionality or capability than your fingertip.