So here is the question I would like to know, do we all work on the same block & whoever finds that block gets the full reward or are we all working on individual blocks ?
Everyone on the planet (except during orphan races) works on the same block.
As soon as someone finds it, we all shift to working on the next, same, block.
You aren't competing against anyone.
When the block changes, you continue what you are doing on the next block, your chances and luck are completely unaffected by that block change.
In fact it's exactly the opposite: when you find a block you are, then, possibly competing against anyone else who also found a block with the same height at about the same time, competing to see who's block will be built upon by the next block height found, i.e. who's block wins and who's block is orphaned.
This is why you needs a very well connected node to the network if you mine to it.
If you use your bitcoin as a wallet (and everyone should run a bitcoin) then the connectivity isn't all that important.
If, however, you mine to it, then the connectivity is crucial.
It's not at all unexpected for a home solo miner to lose orphan races, or even to be mining old blocks that will, of course, be orphans.