Well, yes and no. There is no single app official app dedicated to the NYT Spelling Bee, there are two apps to you can play it on your phone, by using their NYT Crossword App.
Android Spelling Bee App
The first app for the NYT Spelling Bee can be found at the Play Store for Android users. To do so, just click on the link NYTimes – Crossword and you will go to the Play store, and from there, you will be able to download the NYTimes Crossword app. Within the app, as you scroll off the main screen, you will see the ability to download the app and play. You may have to also have a subscription to the New York Times in order for it to work.
iPhone Spelling Bee App
If you are an iPhone user and want to play Spelling Bee on your iPhone, then you should head to Apple’s App Store and download the New York Times Crossword app there as well. Within the app, as you scroll down, you will see Spelling Bee as well. I also think it works a lot better if you have a subscription to the New York Times, in order to keep playing every day.
It’s a little sad that there is not a separate app for Spelling Bee just yet. However, it is fun to know that out of all the other games on the New York Times’ website, this one has broken through and merits inclusion with the famed crossword puzzle.
One quirk I have noticed in both the Android Spelling Bee app and the iPhone Spelling Bee app is if you have the application open before the new day’s puzzle is updated, you will still show you the old puzzle even after when the new puzzle should have updated. That is simply fixed by closing the App (in both Android or iOS) and then restarting it.
is there nytimes archive web page for Spelling Bee, similar to the available archive pages for their crossword and mini ?
Not as far as I’ve found, but you can find older puzzles here on this site.