Question: The highlighted portions are my calculations. I am unsure whether i am going in the right direction or my sig figs are off. Am I supposed to use only 3 sig figs or what the calculator shows?

volume delivered=(final volume from trial 1) – (initial volume from trial 1)

7.50 mL – 0.00 mL = 7.50 mL

mass water=(mass beaker + water) – (mass of empty beaker)

29.691 mL – 22.109 mL = 7.582 g

density water (mass water from trial 1) / (volume delivered from trial 1)

7.582 g / 7.50 mL = 1.01093 g/mL

average density= (density 1) + (density 2) + (density 3) + (density 4)/ 4

1.011 g/mL + 1.003 g/mL + 0.999 g/mL + 1.002 g/mL / 4 = 1.004 g/mL

% error= |theoretical value - experimental value| / theoretical value x 100

percent error = 0.997324 - 1.004/ 0.997324 = -0.00468 \* 100 = -0.47%

[![enter image description here](https://i.stack.imgur.com/RT0Nb.png)](https://i.stack.imgur.com/RT0Nb.png)

Answer: 
Oscar has already explained that your calculations are fine. I see a serious practical problem though. I guess this is a lab experiment for teaching the concept of calibrating a pipette.

I am not aware of any typical 10 mL graduated pipette which can read volumes like 0.03 mL. Are you sure it is a pipet not a (micro)buret? How did someone read 0.03 mL as the initial reading on a pipet? How can one deliver 7.48 mL or 7.51 mL?

Proper calibration work of glassware in classical analytical chemistry requires buoyancy corrections.

Simple rule, don't worry about significant figures until the end. Your balance can read up to 3 decimal places. The calibrated volume by this hypothetical pipet can also be reported to 3 decimal places.
They look right to me except for the percent error calculation. You should render

Precent error = (Measured - theoreticel)/(theoretical) ×100%

Here that would be positive, but you have a negative number so it looks like you turned the formula around.