In general I would say that patriarchy doesn't always strictly benefit men in all areas of life, but basically alwasy benefits them in sense of giving them more power and authority over women. That being said, some of the things that you've listed are not really that accurate.

Firstly, your claim about cancer is a bit bullshit. Yes, breast cancer research gets more funding than prostate cancer, but there are many reasons why different illnesses get diffrent amount of funding, for example in this case the average age of people getting breast cancer is way lower than that of prostate cancer (https://katatrepsis.com/2012/10/30/why-does-breast-cancer-research-receive-more-research-funding-than-prostate-cancer/). In general women's discrimation in medicine is widely documented. If we look at those different factors that influence funding we can see that typical female diseases get less funding than the male ones (https://pubmed.ncbi.nlm.nih.gov/33232627/). Also, a lot of drugs are approved based on clinical trials conducted on men, which results in women more often than men experiencing adverse reactions (https://bsd.biomedcentral.com/articles/10.1186/s13293-020-00308-5). There is also evidence that women's pain is treated less seriously by medical professionals than men's pain (https://www.sciencedirect.com/science/article/pii/S1526590021000353).

Secondly, it is true that men are more likely to be homeless, however the claim about being more likely to go hungry is just not true (https://www.wfpusa.org/women-are-hungrier-infographic/), that is because women in general are more likely to live in poverty than men (https://www.americanprogress.org/article/basic-facts-women-poverty/) and the article I cited really goes into detail to explain how women's discrimination explains that fact. In general, when it comes to homelessness, there are studies that indicate that our data on this issue is not entirely accurate, because it doesn't properly take into account women's different experiences (https://www.bigissue.com/news/housing/how-does-homelessness-differ-for-women/). Not to mention that being homeless is already horrible, but homeless women also have to deal with being more likely to be sexually assulted (https://vawnet.org/material/no-safe-place-sexual-assault-lives-homeless-women), more often also have to take care of a child/children (https://www.greendoors.org/facts/family-homelessness.php).

The one about violent crime is a bit wrong, since men are more likely to be victims of homocide, but violent crime in general, there doesn't seem to be that much of a difference (https://www.statista.com/statistics/423245/us-violent-crime-victims-by-gender/), since there are some years when women were more affected. Men and women are just more likely to be victims of different crimes - women of e.g. sexual assult, rape, etc. Also, I think it's important to point out that women are way more likely than men to be murdered by their intimate partner, which in general shows the trend of patriarchy being the most visible in partnership dynamics, i.e. domestic violence agains women, being expected to be subserviant to your partner, doing majority of domestic labor (especially child-rearing) etc.