I have no idea how to connect the serial port to the chip for programming.
Read the data sheet.

I don't want to use an evaluation board as I think just soldering everything myself I'll learn a lot more.
learn more about soldering you mean!
The beauty of Cygnal eval boars is that it comes with development software, 4k limit of keil c compiler and jtag interface for hardware debug and programming and only at 99$.

3. Compilers - Which is the best C compiler worth its money? I can't afford anything like Keil and I've read that SDCC is buggy.
For learning purposes you can download the eval version of keil compiler (2k limit) which is enough for a quite big program or you can download the eval version of Raisonance c compiler (4k limit).

I just designed an ambulance siren with microcontroller, I used 2 timers, one for the frequency generation and the other one is for the frequency modulation, first timer interrupt togles a port pin and reloads the period into itself, the second timer interrupt changes the period of the first timer reload value at programmed time intervals.
It only took few lines of code and it was so much fun to play with especially when adding an audio amplifier circuit borrowed from the audio equipment industry and experimenting with different sounds and pissing everybody else in the building :

Regards
Mahmood