You can disable the spash screen per application, but only in glide language. In opengl, you have disable it for all programs. To do so, just go into the display control panel, then the settings tab, then click on an advanced button, then go to 3dfxtweaks, then go to the glide/opengl settings, and put a check in disable spash screen. Note you need the 3dfx tools installed to do this. That should do it.
For Q1, it kinda depends on what you mean.. you can use DirectDraw to enumerate display devices available on the computer for finding non-primary accelerators, and you can create a 3D device for that display to find out if it has a Hardware Acceleration Layer and if so, what it supports.