Questions regarding to the mathtex and tex usage


I have two figures, one with mpl’s mathtext and the other one with the latex as seen on the uploaded images:

1-) How can I use the same fonts of mathtext figure (tick and label texts) on the latex one?

2-) When I use mathtext, I always get an extra space after the math term (in my case, after mm^-1). This doesn’t happen when I use latex however I do not know how to use same font for both ticks, labels and equations.

3-) Both in mathtext and latex mode, if the term I use cannot be parsed correctly I get a super long error notifications. Couldn’t this be made friendlier?

Any solutions or suggestions?