Developing BLE device. Questions
First, referring to your existing design, the important thing about a PCB antenna is to have no ground plane under the entire antenna, and to follow the layout shown in TI's application note exactly.  It's not a bad idea to include the Pi network, it may be useful for during RF testing.

You should be able to continue the 50 ohm feed for a little ways, as long as it is surrounded on both sides by a ground place as shown in the app note.

Re the 2032 battery, they are designed for a pulse drain of 15 mA, although they can go higher, say 30 mA, with a minor (9%) drop in capacity.  So you shouldn't need a large cap (although it wouldn't hurt).

However I suggest switching over to a BLE module that has a built-in antenna, like the BLE113 from Bluegiga.  It includes an 8051 which  you can use to run your own application code, and has SPI, I2C, UART, and 12-bit ADC interfaces.

Even though the maximum transmit power is 14.3 mA, this is for a very brief time, and the BLE113 is specifically designed to work with a CR2032 battery -- in fact their development board includes a holder for a CR2023 for testing that configuration.