What is the exact frequency of Delta brain waves during Slow Wave NREM Sleep?
Periklis Y. Ktonas and Atul P. Gosalia performed such an analysis. It was published in 1981 under the heading "Spectral Analysis vs. Period-Amplitude Analysis of Narrowband EEG Activity: A Comparison Based on the Sleep Delta-Frequency Band"

The bins were quite wide but their analysis showed peak power spectrum moved between 0.84 and 1.96 Hz at different times.

I think the paper would serve you well, as it highlights the difficulty in achieving what you have set out to achieve. The frequency is not constant, even over short timescales. It depends for the most part on a balance between the intrinsic, basal polarity of thalamocortical neurons, and the effect of synchronising, inhibitory input from the reticular nucleus. The latter is in turn subject to cortical feedback. There are huge numbers of neurons involved. The period between bursts, and the number of action potentials per burst, is quite variable. 

Perhaps it might be possible to set up a device that alters the round in real time, based on the EEG measurement.

With regards to your 'bonus' questions:

(1) The video posted does show an effect on the thalamic rhythm, which is surprising, as it had been thought that in deep sleep, sound has no effect on the thalamocortical circuit, since it is gated at the thalamus. This shows the plausibility of the hypothesis. However, the video does not provide any evidence that this alteration in rhythm is beneficial. It is possible that it is not and this possibility should be eliminated.

(2) Clearly the sound has an effect on the rhythm, so it seems entirely plausible that there is an optimal sound to maximise the effect.

(3) It will be hard to organise the phase, given the continuous, rapid shifts in period, unless done in combination with EEG in real-time.

(4) I am not aware of any research attempting to correlate thalamic rhythms with heart beat, although it would be quite easy to do. However it is highly unlikely there is a correlation, since the thalamocortical period has a lot of variation moment to moment, whereas the heart rhythm does not. Also the thalamocortical rhythm is generaly somewhat faster.