SD card via SPI: pull-up resistors or dedicated IC?
The pull-up resistors are only there to ensure the idle state (the host will set them to high-Z when the interface is not in use.)

When the SPI / SDIO interface is active, these are driven by push-pull drivers on the host (SCK, SSn and MOSI) and on the SD card (MISO.)

It is helpful to avoid stubs on these pull-up lines to improve signal integrity, but they don't otherwise influence the signal risetime when SD is active.

Be very careful in choosing to add a buffer to the SCK line. This inserts round-trip delay on MISO, which eats into the MISO-to-host setup time. Work instead on optimal routing with good impedance control to achieve sharp edges on SCK and the other signals.

Finally, CD is only a sense signal coming from the SD card socket, not the card itself. How it works depends on the mechanical setup on the socket. Usually it's a switch that closes to ground when the card is inserted.