With iOS 9.3.5 installed, you will have a WiFi Only model of iPad2, iPad3 or iPad mini1.
The 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. Your 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 all obsolete.
You may need to consider that compatible Apps for your iPad are increasingly difficult to find - as App Developers have dropped all support for 32-bit devices and many for iOS versions 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 iPad. As such, if you want or need to access most current Apps, requiring more recent versions of iOS than your iPad is capable, you’ll need to consider replacement of your iPad with a newer or current model.
As for your reported issue with email - I presume you are attempting to use the Google Mail App - instead of the native iOS Mail App. The available Google Mail App requires iPadOS14 or later.
As for using the native Mail App, you should be able to add your gmail account - but be aware that Google have changed their authentication requirements for Google Mail mail accounts configured for password authentication; for non-Google mail clients, now requires use of an App Specific password for each mail client/device.
You will need to generate a unique password for your iPad Gmail account - that will differ from your normal Google Account Password. AOL, Yahoo, Google, Microsoft now all use App Specific Passwords when using anything other than their own email client Apps.
If you need to generate an App Specific Password, you’ll need to log-in to your Google Account management webpage - using a web browser - and generate the Password from the appropriate account security page.
More information can be found here:
https://support.google.com/mail/answer/185833?hl=en-GB
More information about AOL’s App Specific Passwords can be found here:
https://help.aol.com/articles/allow-apps-that-use-less-secure-sign-in?guccounter=1
For Yahoo, more information can be found here:
https://help.yahoo.com/kb/SLN27791.html
For Gmail:
https://support.google.com/mail/answer/185833?hl=en-GB
Microsoft:
https://support.microsoft.com/en-us/account-billing/using-app-passwords-with-apps-that-don-t-support-two-step-verification-5896ed9b-4263-e681-128a-a6f2979a7944