There maybe STILL older apps available to your 1st gen iPad.
You would still need to use the iTunes method to be able to get more apps onto your 1st gen iPad.
There maybe more “up to date”, third party web browsers you can still use that were still supported on iOS 5.1.1 for a much longer period of time nstead of that very old version of Safari.
You should STILL be able to read and send email, using the default iOS Mail app, on that iPad, OR once again try to find another third party mail app that has an older iOS 5.1.1 version still available.
FYI,
The 1st generation iPad was, more or less, an early adopter model iPad.
It was underpowered with only 256 MBs of RAM and NO cameras for image/video shooting or FaceTime calling.
One of the reasons Apple ONLY supported it for one year after its initial release.
If you want to find more useful apps for that 2010, 1st gen iPad,
Not every app you attempt to download will have an iOS 5.1.1 compatible version. For older apps that may still have an older iOS version available, the lowest compatible iOS version of an app is iOS 4.2.1.
The search for iOS 5.1.1 compatible apps will be trial and error, but they are out there.
This website may help you locate the apps you can use with your original iPad 1
http://findoldapps.com/us/any_category/5.1.1/ipad/updated_date/desc/30/1
My 2010, iPad 1 has well over 100 apps on it that are still functioning.
These were apps that I already had downloaded to my iPad 1 years,,ago.
Using the iTunes method and the website link above, you might be able to find older, still functioning apps for that 1st gen iPad.
These are older versions of apps that I currently run on my newer iPad models.
Good Luck!