is it possible to upgrade OS from 9.3.5 on an iPad 2 to higher, and how? some versions of software is not compatible.

No; CDMA units with a GPS can be updated to 9.3.6, but this only patches an issue with the GPS and doesn't improve application compatibility.

(183537)

No, the 9 year old iPad 2 maxes out at iOS 9.3.5.

You can get a current refurbished iPad 7th generation for $279: https://www.apple.com/shop/refurbished/ipad/ipad

Or other older models, but not as old as an iPad 2 for less than that.

Sorry, update to a later major version of iOS isn’t possible. iPad2, iPad3 and original iPad mini cannot be updated beyond iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular).

Apple ended update support for these devices in September 2016. None of these models can be updated to iOS 10 or later versions, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. The 32-bit platform upon which they are built is effectively obsolete.

You may wish to consider that most App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. You may be startled to find that if you reset the iPad (as perhaps you should - before passing it to a new keeper/owner), many Apps that you have now might not be available for (re)installation.

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Even the basic current iPad model supports current iPadOS 13.x - and has hardware specifications and capabilities that will vastly outperform your old iPad

If you decide to properly prepare the iPad for reuse, this is the recommended procedure:

What to do before you sell, give away or trade in your iPhone, iPad or iPod touch – Apple Support

I hope this information is helpful - if only in clearly stating the limitations of your iPad2 and your potential options.