I have 4 but have regularly had anything up to 7 children here (including nieces and nephews, foreign students and children's friends). You can vanquish using a combination of military campaign, enlistment and good humour! (you are doing an amazing thing btw; hope your friend will be OK)
Many things can be delegated. A rota for everything is good. In fact your friend's children might be happy to be involved. Depending on ages of children, things like laying the table, stacking the dishwasher, hanging out washing, putting washing in laundry basket, taking out rubbish, walking dog etc can all be delegated. In fact anything they are able to do can be delegated to them.
Homework: insist on this being done without fail as soon as they get home from school and have had snack. Insist on a rule of no telly before hw finished- it's the only way you can be sure they'll actually have the time to do it without distractions. Ours all used to do theirs at the dining table after snack but before supper, where help was on hand while I cooked.
Hairwashing and baths: depending on ages of children you can have them share baths in appropriate "sibling" groups. Hairwashing can be done as a military campaign even with little ones by lining them up in the bath and doing first wetting of hair, then to back of queue, then shampoo then to back of queue, then rinsing then to back of queue, then conditioner, etc... At my quickest I could wash 3 lots of hair in 5 mn (when DC were about 2, 4, 6)
Re dressing for school in mornings, insist they come down dressed. Drags out too much otherwise.
Re disputes, I would avoid jumping in too soon. Being a listening ear for grievances saves you time and unnecessary involvement in childish disputes but also helps them to work things out for the themselves.