I have one of those old white 2010 Macbooks and I'm wondering if it's worth upgrading the RAM from its current 2GB to 4GB or 8GB. It also seems like the battery needs to be replaced since the count is at 992 and it said, "Service Battery".
As for upgrading RAM, it depends on your typical workload. If you're not currently maxing out your RAM, adding more won't produce any noticeable improvement. If you do need more, your model supports up to 16GB of RAM. This should help:
How much RAM do I need in my Mac?
As for your battery, the "Service Battery" indicator shows when the health drops below 80%. It could also indicate another problem with the battery, but that isn't as common. You can continue to use the battery as long as it holds sufficient charge to meet your needs, as long as it doesn't start swelling, which some batteries do near the end of life. If it does start to swell, have it replaced ASAP, before it can damage other components in your Mac.
The link below should answer most, if not all, of your battery/charging questions, including tips for maximizing battery performance. If you havent already done so, I highly recommend you take the time to read it.
If you're looking to make hardware updates to improve performance, consider replacing your HDD with a SSD. That can produce a more significant performance boost than adding RAM in many cases.
If you're having performance issues, this may help: