Get on! /get off! without the object (the bicycle)?
1 Suppose my friend and I are next to a bicycle:
- If I want have my friend get on the bicycle, can I say "Get on John! / Climb on John! / Hop on John!"?

2 Suppose I am the driver and my friend are next to the bicycle (the bicycle has stopped):
- If I want have my friend get on the bicycle and sitting on the back seat, can I say "Get on John! / Climb on John! / Hop on John!"?

3 Suppose I am next to the bicycle and my friend is is sitting on the bicycle (the bicycle has stopped):
- If I want have my friend get off the bicycle, can I say ""Get off John!" / Hop off John!""?

4 Suppose I am the driver and my friend are sitting on the back seat of the bicycle (the bicycle has stopped):
If I want have my friend get off the bicycle, can I say "Get off John!" / Hop off John!"?

5. In the above mentioned cases, I should use "Hop on John! / Hop off John!", why I shouldn't use "Jump on John! / Jump off John!"?

Thanks!

Question

Get on! /get off! without the object (the bicycle)?
1 Suppose my friend and I are next to a bicycle:
- If I want have my friend get on the bicycle, can I say "Get on John! / Climb on John! / Hop on John!"?

2 Suppose I am the driver and my friend are next to the bicycle (the bicycle has stopped):
- If I want have my friend get on the bicycle and sitting on the back seat, can I say "Get on John! / Climb on John! / Hop on John!"?

3 Suppose I am next to the bicycle and my friend is is sitting on the bicycle (the bicycle has stopped):
- If I want have my friend get off the bicycle, can I say ""Get off John!" / Hop off John!""?

4 Suppose I am the driver and my friend are sitting on the back seat of the bicycle (the bicycle has stopped):
If I want have my friend get off the bicycle, can I say "Get off John!" / Hop off John!"?

5. In the above mentioned cases, I should use "Hop on John! / Hop off John!", why I shouldn't use "Jump on John! / Jump off John!"?

Thanks!

Answer

All of your examples in all scenarios are correct. While the verbs each have their own meanings on their own, in context all are of them are perfectly fine to use though "Get" on/ off can be seen as a command which some people may find a little bit rude (but not every one!).

The only problem I picked up on in your entire question was the use of the word "driver". When you are using a type of vehicle that you sit upon (or even an animal such as a horse) you "ride" it, not "drive" it. It's a minor distinction but if you're aiming for fluency it's an important one.