Is the coin or wallet still being developed or improved in any way, or has it just been abandoned?
DOGE does still have a (passive) dev team - and there have been (few) commits in the last few months - however the coin is one of the most stable in the market - already had 10x capacity of Bitcoin (or 5x capacity of Bitcoin + Sewgit), so not a huge amount actually needs to be done. I know people who practice fundamental analysis love a wallet release.
Info about development can be found here
https://www.reddit.com/r/dogecoindev/most of the community post here - a loose roadmap can be found somewhere in there
https://www.reddit.com/r/dogecoin/