Of course the center differs. From one zoom level to the next, one tile is "split" into four other tiles. Consequently the center of the single tile will be located at the corners of the four tiles. Using the mentioned formula you will always get the tile which contains your coordinates. But due to the nature of tiles it won't be necessarily at the center of the tile. For each specific coordinate there is only one tile at a given zoom level containing it. Hence the coordinate can be anywhere on the tile and not necessarily at the center.
Still I'm not quite sure what you actually want to achieve. For displaying tiles (and markers) all you need to do is using Leaflet or OpenLayers (or any another library supporting the tiles concept).
And keep in mind that MapQuest also has terms of use.
Edit:
An alternative would be to use a WMS service instead of a TMS which does the resizing and concatenation of the tiles for you. With a WMS you just have to define a bounding box around your center and an image size. The resulting image will always be centered around the coordinates. The OSM wiki has a list of OSM WMS servers.
Don't forget to get informed about the usage policy of the WMS service you choose.