connecting flights

I have a couple of questions regarding this process.

1. Does my flight have to be booked through the same carrier throughout or am I able to book two separate carriers (arrival in China and departure in China)?

2. Do my flights have to be round trip (Seoul-Beijing-Hong Kong, Hong Kong-Beijing-Seoul) or can I book a one-way flight to Hong Kong with a layover in Beijing (Seoul-Beijing-Hong Kong) with a separate return flight?

Thank you :-)