Install Chess via the Android Play store.
Download on your sd-card. Long press the link and choose "save link as" if it opens in your browser. Then go to the advanced option of Chess and select Import puzzles.
Daily Chess News and Games. Weekly digest for download. By Mark Crowther.
Choose the PGN column for your download. When downloading on your Android with Chess installed, you can select to import.
Download on your sd-card. Go to the Advanced option in Chess and choose "Import games into the game database". Browse to the downloaded file and select to import. Warning: these sets contain a lot of games, so it can take some time to import them
Download on your computer and copy to your sd-card.
Robbolito (Yakov Petrovich Golyadkin, Igor Igorovich Igoronov, and Roberto Pescatore - compiled for Android by Michel Van den Bergh)
Stockfish (Tord Romstad, Marco Costalba, and Joona Kiiski)
Bikjump (Aart Bik)
More about UCI engines for Android can be found on this website: