Welcome to Android Central.
We kind of need more information to help with your draining issue but to answer your questions;
Yes it is possible to change the battery in most devices. This can usually be done even if the device is sealed.
Yes changing the battery is safe as long as it is replaced with a similar style and voltage battery.
I personally have not used that company and honestly the odds of popping into a random Android forum and finding someone who has is going to be slim.
Now for our questions, unless that was all you needed;
What device do you have?
Is this issue with the fast draining battery something that started or continued after the battery change?
How fast is it draining?
Does the battery percentage indicator fluctuate up and down during normal use?
Does it randomly turn off, even if it says that the phone still has 15% or more charge?
What is an expiration date on a phone? Where did you see this? I think it's safe to say that many people have at one time thought that their device seems to start acting up at about 24 months and while MFGRs will never admit to it Planned Obsolescence happens everyday. Just curious what brought you to this conclusion about your phone?
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