self standing Spa and new pool

[waterbear]

I am not an expert but I don't think the little bit of bromine that might get into the pool would be a problem.
As far as using bleach in the spa, you can. It might be a bit harder to maintain a residual FC than in the pool because of the heat and the bather load in the smaller volume of water, and if the spa is outside you will need stabilizer; but if you shock (throw in some more bleach) after every use, monitor your chlorine levels regularly (run your FC about 2 ppm above what you run the pool at), and keep your water balanced it should be just fine. (not too different from using bleach in the pool after all!)

The water needs to be balanced the same as the pool if you switch the spa to chlorine and you will need to drain it first or it will continue to be a bromine spa. It is recommended that spas be drained and refilled every 3-4 months anyway because of the bather load vs. the water volume so you might want to wait until then...or until you use up your bromine.
di-chlor is the form of chlorine that is usually recommended to sanitize a spa. It is stabilized but you don't have to worry about the CYA levels going too high since the spa will be drained and refilled periodically. Might be the easiest solution. Then when you need to shock you can use bleach for that.
Check out this page on the sister website PoolSolutions
http://www.poolsolutions.com/tips/tip10.html
for info on bromine

I used to have a portable spa that I kept on chlorine for 2 years and then switched to bromine becuase I thought it would be easier. My experience (and I knew a lot less then so that might be why) was that bromine was not easier than chlorine but had it's own problems that were slightly different in terms of water balance. Both sanitizers required the same amount of maintenance, just in different ways.

Hope this is helpful to you.

P.S. from what I can see the Brilliance line by Arch Chemical (the same folks who gave us BAQUA products for pools and spas and the HTH 'dual action' trichlor tabs with copper!) is a bromine/monopersulfate system...pretty standard actually despite all the hype. (Bromine needs either chlorine or monopersulfate to activate it) They keep talking about the 'mineral salts' that is added to it. I would bet money that they mean borates (borax)!