Keepalive mandates that the TCP connection stays open to parse further requests and send further responses and requires the support of the two mechanisms to distinguish the boundaries between different requests or responses (explicit content length and chunked encoding).
Pipelining is just normal usage of TCP, which is a mechanism to establish two queues of bytes between two endpoints on a network.
There is no difference between sending data before or after having received data from the other party. The two directions are logically independent, even if at the transport level data from one direction contains acks of the other direction.
Now, some servers will start processing requests on a given connection in parallel, and will not correctly synchronize the multiple threads trying to write back their respective response to the client. This is just a bug on the server doing multithreading incorrectly, and has nothing to do with any framing problems in the protocol.
I suppose HTTP/2 supports that use case better, since it can multiplex the concurrent responses, but the correct thing to do is to simply treat each request synchronously one after the other, and not parallelize the processing of multiple requests on a given TCP connection.
