The real risk is in you not knowing how to determine "risk"... so let's learn it...
Search "arduino breadboard datasheet"
You will see on one datasheet for a common breadboard, the specifications show Rated: 36V/2A
Remember (really, remember) ONE LED will use 20mA of current at its brightest.
A Neopixel has THREE LEDs (RED, GREEN, BLUE) per PIXEL.
A pixel ring with 16 neopixels will draw (16 * 20mA * 3LED/pix = 960mA) 0.96A, which is less than 50% of the rated value.
This should let you know: NO risk to the BREADBOARD.
You must have an EXTERNAL POWER SUPPLY for this amount of current in your Neopixels (plus other devices). You MUST NEVER use the Arduino to supply more than 40mA of current per pin, or 100mA current per board (multiple pins). For NO RISK, ALWAYS use an external power supply.
AND: Every question about hardware and software, should show your written program (you have that) and a wiring diagram.
What step are we on?
Next step; Writing WORKING code.
Programs should start small, with testing one device until that one device is working as you want. A great place to learning to program for the Arduino is on your IDE's Built-In Examples. (you can also search "arduino built-in examples")
FILE >> EXAMPLES >> BUILT-IN EXAMPLES >> BASICS >>
... and do many sketches from 01. Basics to 07. Display.
Your program has a (1) Neopixel, an (2) LCD and an (3) MPU6050. This is too much to learn for you right now. You should start with the LCD. It displays characters, so it should be the easiest of the three to write a working sketch.
#include <LiquidCrystal.h> // load the LCD library
LiquidCrystal lcd(7, 8, 9, 10, 11, 12); // create an LCD OBJECT and assign Arduino pins to the LCD
void setup() {
lcd.begin(16, 2); // initialize the LCD object with sixteen columns and two rows
lcd.print(" I live"); // send characters to the LCD
}
void loop() { } // do nothing
Your turn... write a sketch for the LCD, then one for the NeoPixel, then the MPU then the "timer." After that, making two devices work together will be the goal... then all devices.