bettas can and will eat shrimp, especially with such a small tank. unless it was heavily planted (which the betta would be left with little swimming room), i don't see the shrimp surviving long.
to lower ph, try DW tannins, or some LFS sell "bottled" tannins. this will darken the colour of the water, but purigin in the filter can help with that. peat moss in the filter as well can lower ph, but brown water. i think you can have the water sit out a day before you add it, but i would test the ph difference with this.