Is there any way to find out that the account numbers are really randomly assigned?

I believe you can use tests available in this link, there are four tests that you can do on frequency counts.

Is there any way to find out that the account numbers are really randomly assigned?

I believe you can use tests available in this link, here are four tests that you can do on frequency counts.

Now for this question-

How would I prove/disprove to someone if one company is actually doing better than another company or if it is probably random chance that one company's rate of return is ever so slightly better than the other company's? In samples of the data the amount of work isn't evenly divided between the two companies

Use t test on mean rate of return between two companies which has lesser rate of return is doing good, If the amount not evenly distributed it doesn't matter, and the problem with normal distribution of rate of return use transformations here is an outstanding blog on how to transform data to normal distribution.

Please comment if you have any doubts or i didn't met the question properly. Thanks!

welch t-test as you said is right way to compare between groups, but if the data is not normally distributed then you have to make it normal by applying some transformations. otherwise if you violate any assumption of t-test results could not be validated.

but in some groups the data isn't evenly divided between the two companies and the data isn't normally distributed.

and i could not understand what this means?

Is there any way to find out that the account numbers are really randomly assigned?

I believe you can use tests available in this link, there are four tests that you can do on frequency counts.