STM32L053C8 Questions on power schematic
Ok, 
Your missing the STM32 schematic itself, to verify everything, we need that.

Next, are you planning on being primarily battery powered?  If so, lose the TLC5940!  If your just wanting to have a few LED available, just drive them from the STM32, if your concerned about using too many pins, have a look at Charlieplexing.

TLC5940:  First off, this thing is a beast!  Unless you need ALL of the bells and whistles it offers, I would start off with something easier, like the TLC59108 or the TLC59116.
Most likely you meant it as a decoupling cap, but that 0.1uF in the VCC line needs to be changed.  Next, how are you planning on programming it?  You need SCLK, SIN, XLAT connected to program it.

The power, SWD, and USB(What type of interface are you using for the USB renum?) all look OK.  Oh, BTW, you can reduce the  100uF decoupling caps down to about 40uF, since your battery powered.  I can't remember the exact App Note, but ST does talk about it.

I've never used that BT module before, sorry.  But there seems to be a slight confusion to my eyes.  It looks like your connecting SPI to the BT module, but that EEPROM is also SPI, and there are no active Chip Selects.  As it is it looks like you'll talk to both at the same time....