My 12V LED strips use about 6W per meter, and the Pi will use about 2.1-3W depending onload. So expect a 9W load. It's certainly possible, but it will be more reliable with a 47uF decoupling capacitor on the input of your buck converter. Since you drive the LEDs from 3V3 transistor control (I presume), make sure the gate/base is saturated completely, or they will get too hot.
The IRLZ44N HEXFET may be a good choice. Make sure you have overdischarge protection on the battery - it can be done with a single 10V zener, or (better), a 10V zener and a NPN/PNP pair to prevent leakage when not sensing voltage. http://www.bristolwatch.com has plenty of useful schematics.
IIRC the SG90 used ~4.5V - you could get by with 4.3V I'm sure. Use the 5V rail on your Pi through a diode, and use a 2N7000 MOSFET to drive it. A catch diode may be necessary.
This "6.8Ah" battery pack can readily supply much more than the ~12-13W your hardware needs.