Back-end functions programming

I need help to create an app. It is for a puzzle/strategy game, similar to chess, i.e. it has 16 game pieces (per player), and each game piece has it's own distinctive movement pattern, on a game area! I have the general requirements as a pdf, so you can get a clearer idea of what is required. For the record this will be for android and apple phones, tablets and other such devices! The main thing is the ''source code'', (back-end in your terminology) which executes the functions. I have the designs of the app UI/UX, game piece model files, etc. Ideally I would like to know the length of development, the depth of development (i.e. how many of the requirements you can fully deliver) without bugs and issues? There is website development part of the idea, which links into the app, but this is pointless unless I get a fully functioning app! If you are more comfortable developing websites instead, then please let me know and make that clear. The cost would also be import, since I am not supported by private investors or established financial institutions. Anything in the ''$XX,000s'' range will be too much for me. Thank you