Hi I just wanted to verify my process for solving this question:

Ok, first of all, I made a diagram to visualize the forces working on the sphere.

To get the Force magnitude of the wind (Fw), I started with the weight of the sphere ( 2.94x10^(-3) N ) and since the sphere is in equlibrium, then the vector Tj is the same as the weight.
Then I used the trig relation Tan(37) = Tj/Ti, solved for Ti and again since it's in equlibrium in the i (x) axis, Ti = (Fw)
For the tension of the cord, I simply used T = (T Cos(37))i

Did I managed to do it correctly or did I completely veered off? Also, did I used the correct vector notation?

Ok let me help you:
[tex] \vec{T} + m \vec{g} + \vec{F}_{wind} = \vec{0} [/tex]
right? so
[tex] - T \sin (37^o) \vec{i} + T \cos (37^o) \vec{j} - mg \vec{j} + F_{wind} \vec{i} = \vec{0} [/tex]