Can you check if a node is pruning? Is it possible to check if a specific node is running the full blockchain or a pruned one?

Also if you can, is it possible to check exactly how many (or roughly) how many blocks they are distributing.
Bitcoin nodes advertise their services with the nServices bitmap. The first bit is NODE_NETWORK which indicates whether a node will be able to serve all blocks to other network participants. 

Pruning nodes do not signal NODE_NETWORK, because they do not have a complete copy of the blockchain. They will however return any requested blocks they have in storage. As the minimum pruning size is 550 MB, they will be able to serve at least the last three days worth of blocks.