@biscuitcat Normally around 9-10 months. But even before this he can have a bottle or cup of expressed milk or formula in the day and should be OK to continue BF in the evenings and at weekends. Your supply will generally cope with this just fine at any point past 3 months ish without you needing to express or anything, as long as the change isn't too drastic (e.g. going from hourly feeds to 8 hours without feeding).
But that said DS2 went from 3-4 night feeds to sleeping 12 hours and my boobs adjusted within 48 hours. The older they are the more "elastic" your supply gets really.
Some babies "reverse cycle" when you start work so they feed more overnight to make up for it which can be draining.
Sharing the load is such a complicated issue I haven't really had time to think about it. I will say that I find DH is very involved but he doesn't tend to do booked type activities with the DC. He is the one who mainly takes DS2 out on his bike, and he will take him out to look around ikea or for a walk or to the park etc. He would also take him to local places like the zoo but I was the one with the year pass and he saw it as a waste of money to pay for entry.
We split wake ups. I hate mornings and struggle so much with them so he gets up during the week and deals with getting him ready for Kita and drives him there before strting work from home at around 8:30. Then I get up at weekends and sit like a zombie with my coffee and the TV on until 9 when we wake him up! Now that he is working I do the afternoon pick up, but since we chose the Kita because it's on the site of his office he picks up if he is working in the office that day. We might experiment with doing certain days in the office and certain days WFH as he has a flexible contract now.
So of course I do all the care until around 4:30 or 5pm when I get back with them both on a weekday. At the moment we are figuring out a new dinner routine to include DS3 but previously he would quite often (70% of the time?) prepare food and even recently get DS2 to help him cook which he likes. I'm generally frazzled at this time of day, between 3-5 I just have a huge slump in energy levels. I think I'm going to have to get into some dinner prep earlier in the day.
He does probably 90% of the day to day cleaning 
He fills the dishwasher, DS1 empties it, he tends to wipe down the kitchen sides and collect stuff from around the house. Every night before bedtime he gets DS2 to help tidy up and then runs the robot hoover in the front room. I try and currently fail to keep up with the laundry, and some days do a bit of cleaning in a random room. I deal with all their clothes, sorting, buying new, knowing what sizes they are in, deciding what to do with old ones. I love doing that and wouldn't want to share it. I also tend to be the one to research big purchases like car seats, buggies, furniture etc although of course he might have input or ideas.
He currently does all the baths with baby as in gets in the bath with him. Although he is getting more and more splashy and adventurous so he might need to stop soon. But I really like this and it's something we've done with both of them and even my ex did with DS1 when he was tiny. Nappies at weekends are probably 50/50 as we roughly alternate. We facilitate each other to have a nap basically whenever we want because I think it's helpful. That means that he has periods of being in sole charge as well. I would have no issue going away and leaving him for a week as I know he would handle everything fine. (I wouldn't because of breastfeeding, but I know if I did he would feed formula and it would be fine). If you can't do this, then it's worth looking at what specifically would be a problem and working on that.