Few questions.
You need more capacitance on the battery side, add an extra capacitor on the battery input, 100uF 6.3V SMT caps will help as the battery ages or if you have a poor holder connection. Same on the main bus as well, extra decoupling will help.
What is the function of Q1, R12 and R13? They serve little function as far as I can see, unless you want to lose some voltage, where a smt inductor to filter the line a little would be a better bet, using almost any value of inductor with low DC resistance.
As to using SD or microSD, choice is yours as to how big a footprint you want to have on the board, best will probably to have a SD card footprint and place the microSD card footprint inside it so you can choose during assembly which adaptor you want to solder in.