iPad 2 won’t download any apps

Would this be an iPad2 as stated, or an iPad Air2 per the tags appended to your post?

iPad2, iPad3 and iPad mini1 can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).

Apple ended update support for these models in September 2016. These models of iPad cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed; these are 32-bit architecture devices, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms. iPad2, iPad3 and iPad mini1 are obsolete.

You need to consider that compatible Apps for your iPad are increasingly difficult to find - as most developers have ended all support for 32-bit devices and are increasingly dropping support for older versions of iOS preceding iOS11/12/13. As older versions of Apps are removed from the Apple App Store, you’ll not be able to (re)download or install them - which may severely limit the usefulness and utility of your older model iPad. As such, if you want or need to access most current Apps, requiring more recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model.

Of current models, even the entry-level iPad8 has specifications and capabilities that will massively outperform your iPad2 - and is compatible with the vast majority of current Apps. Other models are more powerful still.

I hope this information provides helpful and succinct clarity as to your available options - and the potential limitations of your current iPad.