Alrighty,
I will try, once more, to offer my assistance and sage advice to you that has work, already for quite a few iPad 2/3 owners to date.
FIrst, I need some info.
What storage version model iPad 2 do you have and how much free space is left on it?
When you surf the web, how many active tabs do you leave up an running?
How many background apps do you leave up and running in the App Switcher?
Next,
What kind of Mac are you using, what year, screen size, what are you running for OS X version, how much RAM installed?
This later info is so I can determine if your Mac CAN or CANNOT be upgraded to a newer OS X version that supports the newest update of iTunes.
As a first step to help with your issues, I will state IMSO, that Safari on iOS is not great to begin with and has always had issues. That is why I stopped using it as my primary web browser of choice many years, ago. I am not that crazy about Safari on OS X. The iOS version seems worse for some web browsing tasks and on some website that I regularly visit.
Second, FireFox for iOS (and Android for that matter) is a utter crawp web browser. Total garbage. Total disaster (unless this has changed recently).
It bears NO resemblance, AT ALL, to FireFox on the main computer platforms. Mozilla group shouldn't even call that web browser Firefox! That is how bad I feel it really is!
Same goes for ANYTHING Google related. Googlewares are resource hungry, RAM sucking coded disasters of software and should be avoided on any iOS device and on OS X.
I use other third party web browsers that have been with iOS for a much longer period of time and have hd a LOT more developement time.
I use a third party web browser called Perfect Web browser, it has a downlaoder bulit-in, looks and works like a normal computer web browser.
I relegate Safari as a backup, alternate browser, if I need it.
Other long term, third party web browsers are Atomic Web Brower, Dolphin Web browser, Mercury Web Browser, and one or two others that have been around almost since iOS and/or versions for when the iPad was first released in 2010.
Not ALL third party web browsers work alike just because the use the same iOS developer tools.
As much as I hate repeating myself and posting the same info, but it maybe quicker than hunting for this info inside of this posting.
Here is a list of things you can try that I have compiled and continually update.
I used some ot these early on when iOS 7 was introduced as this is when iOS was starting to slow older iDevices down.
These have help my iPad 2 and 3 performance and is a intial set of suggested solutions to try (try them all together) before I list my own, MODIFIED backup/restore process (which will need the latest iTunes which will need an OS X upgrade to accomplish, if your Mac qualifies, I can post OS X upgrade procedures for you, as well).
Try resetting All Settings found in the Settings App under General and in the right column under Reset.
Try resetting histories and deleting/resetting caches in all of the web browsers you use.
If you use Safari, these functions maybe in the Settings App under Safari.
Other web browsers have their settings inside of the running app, itself.
If your iPad has been activated for iCloud, in the Settings App under iCloud, to the right, under iCloud Drive, tap iCloud Drive and make sure Safari is turned off for saving Safari data to iCloud Drive.
CHECK FOR THESE SETTINGS NO MATTER IF YOU ACTIVATED ICLOUD OR NOT! It may make some difference.
Also, under iCloud in the Settings App, in iCloud Drive, disable the saving feature for any other apps that you DO NOT want data being saved automatically to iCloud Drive.
If using Safari is still causing issues,
Try changing/using another, different third party web browser.
I don't use iOS Safari too much any longer because I found it causing me some headaches on certain websites I, regularly, visit.
I commonly use another third party web browser, Perfect Web Browser (there are others that may suit your web browsing style better, so look at all of them first to see which third party browser may work better for you) and I never experience a lot of the issues that Safari was causing.
In the Settings App under the General tab, to the right under Spotlight sesrch, try disabling the search under apps that really do not need a search, like some games, remotes, apps that really do not need to be searched, etc., to reduce the list for Spotlight to search.
Try turning on Reduced Motion.
This is found in the Settings App in the General tab the left panel.
In the right panel look under Accessibility, the look for Reduce Motion and turn this feature "On".
You should see an appreciable performance increase on all iPad 2, 3 and 4 models.
In the Settings App under the General Tab, in the right column, look for Background App Refresh and turn this setting to "off".
Some users have suggested that turning off Find My Phone/iPad has helped with performance issues, too.
You turn this off in the Settings App Under iCloud.
Try this one only as a last resort because it is better to have this on as a way to track your iPad in case of theft or you take your iPad somewhere and forget it.
As a last step, Try another hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.
Good Luck!