In each case, it would be best to use "to" instead of "onto":
Can you tune the radio to BBC?
Can you switch the radio to BBC?
Can you turn the radio to BBC?
This is because "onto" expresses movement to a surface ("move onto the pavement") whereas "to" can express movement towards a condition or state (in this case, the state is the radio receiving BBC).
You could use any of these, but tune is the most commonly used. It is acceptable to use turn and switch, but less common. I expect turn will become increasingly less common as more and more people move from analogue radios to digital ones, as turn refers to turning the tuning wheel/knob on the radio to a particular frequency.
For the second part of your question, it is acceptable to "tune" a TV to a particular channel. However, I would again expect this to become less common as analogue televisions become a thing of the past.
It is correct and common to say "turn the TV to channel 9."
Keep in mind that relative usages of the terms can and do vary greatly with region. I would not be surprised to hear any of the combinations mentioned in your question, but some regions may use one more than the others.