So now two kids in my house, seems relevant to ask for more deposit under the circumstances.

A realistic summation of the financials, tailored to whatever the circumstances are the house presents.

However in most circumstances I've seen, the tenant takes the space and completes the fit-out on their own with their own Architect/Engineer & Contractor. 

The example you cited is likely to be very rare, I do not know the circumstances surrounding it but my guess would be that that deal was financed for 5 years, maybe 10 or whoever got it was extremely fortunate.

Will he/she ignore that to always calculate in some reserves or will those mitigating circumstances actually be considered?

Regarding interest rates, all of the options you've listed are very reasonable depending on the circumstance. 

That falls in the "extenuating circumstances" category.

I know it's unorthodox to pay for a bpo, but given the circumstances and wanting to be respectful of his time, how much do you think would be fair to offer to compensate them for the bpo?

I'm a deep South gal at heart, specifically HOTLANTA, but circumstances moved me to Central PA and my REI blood, sweat, and tears paid off in a big, personal way.

And I would also say that you will get a lot of great guidance on here.Regarding vacancies, I think that is a personal choice given the circumstances.