Sounds like 2 issues to me :
1. you didn't replace the CPS sensor with a Bosch branded one, do so.
2. either the battery IS bad, or you have a ground cable issue, or the guy lied about the alternator.
Do this :
Get yourself a cheap multimeter ( usually < $15 ) and measure ohms from the negative battery terminal to a good clean place on the engine. It should read pretty close to 0 ohms.
Then use the meter to measure volts across the 2 battery terminals with the car off, you should see 12.1 to 12.5 volts.
Now start the car and do same measurement, you are looking for 13.7 - 14.2 volts, which would indicate the alternator is working.