First, depression. The correlation between unemployment and depression has been studied since at least the 1980's. One issue that has been considered but never completely explained is the "direction of causality." In other words, does unemployment cause depression, or are depressed people more likely to be left unemployed? Some articles suggest the former, while others suggest the latter; it may well be that both are true. From what I've seen, much of the research focuses on the impact of unemployment on mental health. Here's a Forbes article which is a bit more approachable:
https://www.forbes.com/sites/susanadams/2014/06/09/how-unemp...
If you'd like, you could dive into some of the relevant research articles yourself. Here are a couple articles I found that may be relevant:
https://link.springer.com/article/10.1007/s00420-016-1178-7
https://www.cambridge.org/core/journals/psychological-medici...
http://neuro.psychiatryonline.org/doi/abs/10.1176/appi.neuro...
http://ps.psychiatryonline.org/doi/full/10.1176/appi.ps.55.1...
https://academic.oup.com/ije/article/28/1/95/777542/Unemploy...
There are probably better sources out there, but as I said, I'm no expert and I'm not up-to-date on the research!
There are several challenges facing research into the relationship between unemployment and depression. For one thing, depression can have a number of other causes, and associated risk factors. It can be hard to pick apart the causes from employment status. Another issue is gathering data. Many companies here in the US will ask for voluntary self-identification when a candidate applies; often, however, depression is considered to be in the same category as other disabilities so that it's impossible to pick apart the rate of depression among candidates from the rate of disability among candidates. Another issue that applicants may decline to self-identify. Some companies are better than others at gathering data about depression among workers, and trying to help those employees.
Next, transgender. Here, the research is less well-developed. The transgender population is rather small, so data-gathering hasn't been a high priority until recently. Most data comes from survey of transgender individuals rather than from employers. There may be some inherent bias as a result, but at the moment it's really the best data we have. I'll point you to the National Transgender Discrimination Survey, which was released in 2016 based on data gathered in 2015:
http://www.transequality.org/sites/default/files/docs/resour...
The report is rather long, but it had several important findings: 1) Transgender employees have double the rate of unemployment as the average. 2) 26% reported being fired due to their gender identity. 3) 90% reported harassment at work. 4) The effects compounded with other factors such as race or poverty.
It's worth noting that many states in the US offer no or few protections against LGBT employment discrimination. Here's a map to show how protections differ across states:
https://en.wikipedia.org/wiki/LGBT_employment_discrimination...
I won't touch the degree issue; it's been discussed plenty elsewhere on hacker news, and there's still the mentality that candidates with degrees are better than candidates without.
Sorry, these are completely different things and frankly sounds like nonsense.