If you are talking about pinkie mice, that is definitely too small of a meal for your BP. Hatchling corns can eat pinkie mice, and they are about as big as a pencil. Most people who feed pinkie mice to BPs are either feeding them just enough to keep them alive until they sell them, or in some cases they just don't know better.
A more appropriate meal for your BP would probably be at least a hopper mouse, and it could probably take something a little bigger than that.
It is recommended to give your new snake a little more time to get acclimated to her new home before handling her. Since you have had her a week, you could go ahead and try to feed her. If she eats, great! Wait 48 hours for her to digest, then start handling her with brief sessions every few days. Most likely, she will start to calm down soon, but be patient with her. Remember her instincts are telling her that when something big picks her up, it is because she is about to become dinner. No wonder she is terrified!
If she does not eat, do not handle her other than the minimum required for tank maintenance until you've got her eating. Handling her is stressful to her, as I explained above, and snakes that get too stressed won't eat.
Also, you can get digital thermometers and hygrometers at pet stores, but you'll get the same functionality for less $$ at walmart.
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