I don't even ask about cooking or washing skills.
I should jolly well hope not! You're not interviewing women for a housekeeping job. As you get to know somebody and spend time with them you'll see whether they have any cooking skills. What's this about washing?? You don't mean laundry surely? Or do you mean cleaning? What are your own cleaning skills like? Every person, man or woman, should know how to do basic cooking, how to budget for a week's shopping and plan daily menus and how to maintain a house to an acceptable level of cleanliness.
Personally, I can't abide men faffing around in the kitchen although I do permit my husband to make breakfast on Sundays. I also prefer not to be 'helped' with housework as men are usually more of a hindrance. I'm quicker doing it myself. I blame their mothers. If men were properly brought up and taught how to look after themselves they wouldn't be so useless but mothers waiting on their children hand and foot are the root of all evil. Also, women are multi-taskers by nature. We have to be. Nature designed us to be able to watch over young and do other things at the same time. Any woman worth her salt can cook dinner, supervise the kids' homework and do the ironing, while making a mental shopping list for tomorrow's groceries. A man can do one of those things, not very efficiently, and that's just the way they are.