This app was mentioned in 4 comments, with an average of 1.50 upvotes
On Wikipedia it says Google Play Store (or Android Market, as it was called back in the day) became available to users on October 22, 2008. Googling with queries like "android apps available in 2008" (not necessarily with quotation marks) provides several "most popular apps" articles from that year, like this and this. In particular this article lists popular apps as early as November 2008, showing top picks to be Pac-Man by Namco, MySpace Mobile (no longer available), The Weather Channel, ShopSavvy, Ringdroid, imeem mobile (shut down by MySpace in 2009), Shazam, Rings Extended, Bonsai Blast, and Brain Genius Deluxe (the two last seemingly no longer available).
Judging by this selecting (and assuming I've found the correct Google Play links) it appears that the Play Store still hosts several of its first apps. Chances are however that many of them suffer compatibility issues on newer devices due to lack of updates. On a side note, the absolutely first apps on Google Market were probably Google's own, and many of these, such as Google News, are still in use today.
Absolutely! Here it is for Android:
https://play.google.com/store/apps/details?id=com.namcobandaigames.pacmantournaments
The key is to find something that keeps your mind engaged and distracted!