Dolphin Browser is indeed in the Google Play Store, but it's now marked as "Your device isn't compatible with this version." It will only show up in the search list if you start typing the exact app name, and then choose that specific app from the list. However, the mini and pad versions are compatible and will show up if you do a general search.
And yes, I'm pretty sure that if an app goes from being compatible to not compatible, it won't show up on your previously downloaded apps list. If I remember right, I think that happened to me a couple months ago, but I forget what app it was.
To update apps not originally downloaded from Google Play, obviously go to the source from where you first got it. If it's an alternative app store and you use their app to access it, that app might have an auto update service. At the very least it will probably have a manual update notification area. Just visit that app store occasionally to check on updates.
The alternative that I use most often to download apps that Google Play lists as incompatible is 1Mobile Market. Download their app store app from
www.1mobile.com. (Their app is available on Google Play, but it's marked as incompatible, though works fine.) They have the regular Dolphin Browser available, so you can download and update it from there. (Other legitimate app stores that I use are Amazon and SlideME Market.)
Sent from my Nexus 7 using Android Central Forums