[OccabsLam]

See also Mufti Muhammad's answer which was posted there also: http://www.ilmgate.org/are-the-proph...-their-graves/

So, taking into account the following paragraph:

Is it correct to say that the Prophets عليهم السلام and the shuhada' (and anyone else who has this honor) are alive in their graves, and what separates that "life" from the "life" of the barzakh is the degree of how close they are to the dunyawiyyah life, i.e. the strength of the connections between the body and the soul? And from excerpt of Takmilah Fath al-Mulhim, that the strength of the connection would be stronger for the Prophets than for the martyrs, etc., on the basis of superiority?

I am just trying to clarify my understanding.

Your understanding is correct. Mamaatis do not differ regarding the modality of this "life" as they sometimes suggest, but rather they go to the extent of saying that there is no connection of life with the blessed body of the Prophet (sallallahu alayhi wasallam). Some Mamaati scholars have audaciously told people there is no point of sending blessings at the Blessed Rawda of the Prophet (sallallahu alayhi wasallam), because he can't hear you anyway. This is the real issue here.

[HaroldMY]

Yes the degree of life are different as like connection of soul with toe & with hand & with eyes. The soul are connected to all three but the degree varies as if you get a cut in toe the pain would be comparatively less than those from hand & so on..
the brief explanation is given by Maulana ilyas guman http://www.ownislam.com/video-bayan/...aw-azad-kasmer
if link doesn`t work,put "aqeedah hayatun nabi in peer mahal" or http://www.mefeedia.com/watch/20364108 or www.youtube.com/watch%3Fv%3Df8IlaaYZyhM