During busy days & nights, I have an option to complete my sleep and get up late or get up at my usual time & focus on completing daily tasks? Which one is more important out of the above?

From everything I know. Your sleep is one of the first steps to everything else, so if you would be sacrificing your sleep for waking up earlier and doing your tasks – it's not worth it.

if your sleep quality wont suffer from it then it should be fine

Staying up getting up late will help you put music on your phone and listen to that and get the chores done I found that as a well it helps me.

Really depends on your needs but in general it’s a better idea to get proper sleep so that you will have the energy to work still. Even if you start your day late, it’s always better than never starting plus you can always delegate chores to another day as needed. Often life happens & my errands/work/house chores get tossed around to a day or two late but at least I’m rested & better able to deal with it then.