620 square inches is enough floorspace - about 75cm x 50cm. Although it depends on the dimensions of the cage/tank - some are only about 30cm deep and longer, which is too narrow. But something like 75 x 50cm or 80 x 45cm is fine.
I would be a bit concerned about the 3 levels as it sounds quite high. Falls are a big risk especially for small dwarf hamsters - if they happen to climb and monkey bar across the roof in the night they could have a long drop and hurt themselves or bounce of the edges of shelves on the way down.
So if it's a tall cage it would be better to have one full level to make it safe. You might be able to create this using the existing shelves (ie have two at the same level, a ladder at one end and put a piece of wood or something to cover the whole of the gap between the shelves, except the small bit at one end where the ladder is - then put a small shelf over the ladder entry (so they can't fall from the top down the hole).
Cypher has said it all about the cleaning etc. Weekly clean outs aren't necessary - you can easily go a couple of months spot cleaning and emptying a potty, before needing to do a substrate change - and then try and replace some of the old substrate and mix it in so it smells familiar. Then do the wheel a different week and the toys etc a different week again (toys don't need doing that often usually). Also, as Cypher says, don't throw away the nest and hoard. I just leave them unless they're pee'd in. They tend to only hoard dry food. If you do have to remove them because soiled, try and leave a bit of the old dry nest and put a big heap of torn up strips of plain white toilet paper out in the cage so she can forage for them and rebuild her nest. Also replace any removed hoard with new food in exactly the same place. They get very anxious about their hoard and nest. It's instinctive to them to hoard, forage and nest so they always have emergency supplies.
Don't worry about poops - they sometimes eat them (normal) or hoard them - they have two stomachs and can redigest vitamins etc from the poops. Poops can be emergency food supplies! They are just like little hard black seeds and not smelly or dirty - so unless they really start taking over in a big way you can just leave them mostly - and spot clean if they do take over!
I wouldn't do the litterbox every day - maybe every 4 or 5 days. It's instinctive to us humans to want things neat, clean and tidy - but to hamsters it's like being invaded by cleaning ladies
Or like coming home and finding someone has moved all your stuff and you can't find it and everything smells different and not like your home.
Main thing is to have enough depth of substrate so the cage stays clean longer. Also it helps if they have a house that is on top of the substrate and open underneath. That way they can have more normal behaviours, which is to bury hoards under their nest (and snack in bed) and burrow down to keep warm. It's also more hygienic as doesn't get condensation inside that way.
A house with a lift off roof is nice too - not essential but it means you can check inside without having to take the house out and their nest falling apart. A shoebox house is good - use the lid as a lift off roof and cut the base out and a hole for a door. Although a shoebox may be a bit big for a dwarf hammy - unless it's a child's one.