What should I do as Mongols in early castle age?

I lose a lot of games after gaining a huge advantage in feudal age because I don't know what to do in castle age even when I get there first. I usually scout rush, most of the time successful. Then I follow up with archers and/or skirmishers. Often times at my level (1070 elo) where everyone tries to fast castle I do devastating damage. In the worst cases I hit a castle time similar to them, usually earlier. However, once they get to castle age I am in trouble. Unless I have a huge lead and just kill them with crossbows the game drags on for a long time. I lost games after having a 15 villager lead in feudal age and getting to castle a minute or two faster.

They either amass a lot of skirmishers and kill my crossbows or manage to get enough knights out to kill my crossbows while I struggle to decide what to do. I know going for mangudai early is a good thing to do but they still die against skirms and you need a lot of them to really stop a group of knights. Also, getting castles up while still building town centers and units seems hard. I tried going for my own knights or camels but the food and gold are needed to get upgrades and mangudai. My questions are:

How do I deal with a lot of knights or a lot of skirmishers as Mongols?

When should I go on stone and how much to get a decent castle timing while not tanking too much economy?

Is it worth it to switch into something else (like camels vs knights or skirmishers) before mangudai?

When should I stop archer/crossbow production and completely switch to mangudai?