Learn English – Change to passive voice

Number (2) is fine, correct and natural.

Number (3) should say, 'Some money was given to her.'

Number (5) is close, but the 'to' should be replaced with 'by him': 'She was given some money by him.' However, you could omit both so it's exactly the same as Number (2).

Number (6) is fine, correct and natural.

As for the best way to get this into the passive voice, I would say 'She was given some money by him' is your best option.

The passive applies as though auxiliaries were not present, and then any auxiliaries take part in subject-auxiliary inversion just as they would in an active sentence. This is one of the arguments for deriving auxiliaries from outside the core part of a sentence (by a version of Subject Raising).

So, without passive, we have

1. will [ someone offer courses ]
2. someone will offer courses (by Subject-Raising)
3. will someone offer courses? (by Subject-Aux Inversion)

And with passive, we have

1. will [ someone offer courses ]
2. will [ courses be offered by someone ] (by Passive applying to lower clause)
3. courses will be offered by someone (by Subject-Raising)
4. will courses be offered by someone? (by Subject-Aux Inversion)

Examples with more complicated sets of auxiliaries work the same: "Courses should have been being offered" = "Someone should have been offering courses".

This is an outline of the treatment in McCawley's TSPE.