Intuitively, I feel that these two ragas viz. Bageshree and Kanada do not seem to gel.
Let us see phrases of both these ragas which in my opinion do not match:
a. Bageshree goes with Ma-Ga (komal)-Re and Kanada goes with Ga (komal)-Ma-Re.
b. Phrase Dha –Ni (komal)-Pa has shuddha Dha as in Bageshree while komal Dha in Kanada No doubt Ni (komal)- Pa-Ma-Pa is a Kanada phrase but it does not match with Dha-Ni (komal)-Dha Ma-Pa of Bageshree. In any case komal Dha is just not used indicating Kanada ang.
c. Ni-Pa-Ga (komal) (with a ghasit of Kanada) do not match with Dha-Ma-Ga (komal) of Bageshree.
d. Some musicians use the phrase Sa-Ga (komal)-Ma-Pa as in Bhimpalas with Pancham as a resting point to indicate Kanada, which I think is unsuitable.
I find that the mood of Bageshree and Kanada also have a differing approach. It is not easy to define what sentiment raga Kanada conveys, as there are so many prakars having deferring undercurrent (rasa). I find Bageshree on the other hand, has a mood of shanta rasa in purvang and adding Pancham and a touch of shringar in the middle octave. Hence your 2nd question- how to balance between Bageshree and Kanada becomes irrelevant in view of what I stated above.
Sankirna ragas are matched in 3 ways:
a. one raga in arohi (asect) and another raga in avrohi (descent)
b. one raga in purvang and another raga in uttarang
c. mixing of ragas without any specific framework meandering during execution to slip from one raga to another.
d. Frankly, I do not find anything worthwhile to balance these two ragas as there are so different.
When you consider my above remarks, response to your question no. 4 becomes unnecessary.
However, melodic movements of Shahana Kanada and Bageshree Kanada are so different. In Shahana though it is known as Kanada, I don’t find any marked flavour of Kanada.