"An entity must not engage in legal practice in this jurisdiction, unless it is a qualified entity"
If that is the actual wording of the offence, then the charges are not only warranted, they will succeed when prosecuted. This is all about "representation".
"We act for ...", "We request ...", "We are instructed ..." - These all imply that "A" is representing "B". The fact that "A" is an individual and that "A" is the same individual as "B", is totally irrelevant. By sending letters that claim, or in any way imply, that "A" is representing "B", "A" has engaged in "legal practice" and did so whilst not being a "qualified entity".
If the above is the correct wording for the offence, then you have no chance of successfully challenging the charges or having them dropped. It's just not going to happen on it's own.
Given that there are also three counts of attempting to influence a witness and these appear to be related to the same events, your best chance is to get professional representation and see if they can organise a plea bargain to have one of the sets of charges dropped, which would obviously mean pleading guilty to the other set. This is by far your best option.