This app was mentioned in 4 comments, with an average of 1.25 upvotes
M:tg Tracker play store does all of that. There is a free version, but for the features that you need, it will cost you a couple of bucks, I think.
You can even set TCGPlayer as your price engine.
I use M:tg tracker for stat keeping. I use my lgs as players name and keep track of my win/loss ratio with each deck that I play.
https://play.google.com/store/apps/details?id=net.shalafi.android.mtgpro
I also use MTG familiar for all my trading.
For the timestamp thing, take a look at this app https://play.google.com/store/apps/details?id=net.shalafi.android.mtgpro&hl=en
Actually download it and try adjusting the life total. You can see how they group the changes into "-3", "+5", etc... next to what the new life total was. It helps minimize the biggest disadvantages of using an app vs pen and paper.
Also, in regards to all the other comments, there's a million life tracker apps that can pulling in card pricing info. The one I linked to does that. That might be a nice coding challenge, but if you can make a simple, functional app that doesn't need a milion permissions like accessing the internet, you'll have a great, unique application.