The (native) ext4 filesystem is said to be robust with respect to power outages (ref.). I'd guess that file system corruption due to a shortcoming of ext4 is less likely than random corruption of your SD card. If that's true, consider spending a bit more for a high-quality SD card & don't worry too much about tweaking the filesystem. Maintaining a good ...
Pins 2 and 4 are both on the 5V power rail. You can consider them to be the same pin. Just as much power will come out of pin 2 as pin 2 and 4 together.
It might be worth connecting 5V power to both ends of the LED strip.
As joan has answered you NEED to share a ground to the control interface of your servos.
How this is done is dependent on the physical layout of the wiring, and is somewhat of an art.
Ideally the control interface and servo power should not share any wiring, as any voltage drop in the common wiring will be introduced into the control interface.
The best ...
You need to connect the Pi ground to the servo power supply ground. You will not be able to control the servos unless you do so.
I have controlled a robot arm with 5 servos. I had to use an external PC power supply to get the amperage needed at 5V.
First, if your RPi works fine (you don't get undervoltage warnings), then leave your setup as it is. Don't try to repair that ain't broken.
Second, it's actually not such a great idea to power down the RPi without using the "shutdown" command. So, if you're going to get a separate power supply for the RPi, consider leaving it powered at all times, even if ...
If you only connect to header pins with the power off and/or use insulated dupont connectors there is no problem.
If you aren't using the power pins just put an insulated connector on the power pins. There is little risk using the actual GPIO pins (you have to connect 2 outputs of different levels), but even there connect with the power off.
Most people ...
The Pi's 3V3 (pins 1/17) and 5V (pins 2/4) pins are NOT GPIO, they are part of the power supply rails.
If you connect the 5V power supply rail to the 3V3 power supply rail you will destroy the Pi. There is no protection.