I'd like to get ore, and place it (without command blocks) anywhere near the contraption. My question is could it be possible to do this, and if so how?
Note: it does not matter on the timing the block comes out, as long as I don't have to wait 15 minutes or so.
Minecraft with no mods and no command blocks has no way for mechanisms to place regular building blocks at all.
However, dispensers can place a few specific types of blocks, all of which are somewhat special:
Some related things that are possible, but are not actually placing blocks that were items in a chest:
A cobblestone generator mechanism can produce a supply of cobblestone one block at a time which is pushed where it is wanted by pistons.
Plants grow into spaces made available for them, and their growth can be blocked by piston movements and then accelerated by dispensers loaded with bone meal. (This could be used to abruptly grow a tree, for example.) However, it is not possible to place a new plant except by hand.
Dispensers can place boats, which are entities but (unusually) are solid enough to stand on.
In Minecraft, most blocks are impossible to place with redstone. However, you can always use a cobblestone generator to generate cobblestone and use pistons to push it to a certain area if you want.
