Why not. can a nominated person be a AM for different AOC? yes. due that, my guess is YES

Yes, it´s allowed.
There aren´t any restrictions CAMO.A.125.

No restrictions in Ops rules either.
For Ops related questions, consider writing to air_ops@easa.europa.eu who will redirect to a subject matter expert.

Yes, it is possible.

In according with ORO.GEN.210-point (a) of Regulation (EU) No 965/2012, the operator shall appoint an accountable manager, who has the authority for ensuring that all activities can be financed and carried out in accordance with the applicable requirements. The accountable manager shall be responsible for establishing and maintaining an effective management system.
Moreover, in according with GM1 ORO.GEN.210(a):
(a) The accountable manager should have the overall responsibility for running the organisation.
(b) When the accountable manager is not the chief executive officer, the competent authority should be assured that the accountable manager has direct access to the chief executive officer and has the necessary air operations funding allocation.

However, the Accountable Manager has to nominate a Flight Operations Manager that fulfills the requirements set in GM2 ORO.AOC.135(a).

In your case there can be two scenarios:

A. Nominate one FOM that fulfills the requirements of GM2 ORO.AOC.135(a) - point (c), meaning both airplanes and helicopters flying and operating experience and licensing.
Or,
B. Nominate one FOM that holds a flight crew licence and the associated ratings appropriate to the airplane operations and a deputy FOM that holds a valid flight crew licence and the associated ratings appropriate to the helicopter operations, or vice versa.

Hello Chet, apologies - I'm afraid I do not know the legal situation, but I think the answer depends on your country's primary legislation (civil aviation act etc). That's because, as far as I know, Bhutan has a Technical Co-operation relationship with the EU Aviation Agency (EASA). That does not mean that Bhutan has adopted EU aviation requirements, so the answer could lie with your national rules.
In EU rules, there should not be a problem with one AOC covering aeroplanes and helicopters - it is quite common in the EU and associated EASA states.
It might be useful to connect with carlos.menendez-de-solas@easa.europa.eu, who is the EASA project manager for the South Asia project (including Bhutan) and maybe he could help.
Sorry if I have muddied the waters!
Aviation isn't usually this complicated!
Best wishes, Chester

Thank you all for the valuable comments