There are a number of things you can do and avoid doing, to help her settle in and relax and gradually become tame and feel safe/bond with you
1) They can be very territorial about anything entering their cage - and can be much better out of the cage in that respect. Usually when they arrive you should leave them alone for 2 to 3 days to adjust to the cage environment and scent mark, and then start by offering the odd treat through the bars and talking to them gently. Also don't move things around in the cage or do any clean outs for the first 2 weeks. So if that wasn't done at the start she may have continued being stressed and a bit too territorial.
2) Is her cage big enough? If not this can cause cage aggression.
3) Avoid doing big clean outs - it's not necessary and stresses hamsters a lot - especially younger ones. It removes all their scent marking and seems strange and unfamiliar,plus makes them anxious that a predator has been in there trying to steal their hoard! If you have a good enough depth of substrate (which is good for hamsters anyway), then you can just "spot clean" - ie remove the odd handful of soiled substrate and replace it with a clean handful and mix it in. And only do a substrate change every 2 to 3 months really - especially if you use a litter tray - they will use it if it's in the right place and then the cage stays mostly clean and dry so much less cleaning required. Also even when you do a substrate change, don't clean everything at the same time (wheel can be done a different week and toys infrequently as and when required) - so something always smells familiar.
4) Nest and hoard - these are the hamster's most important things and they get stressed if these are removed. Unless they are pee'd on there is no need to remove the nest and hoard. It can last a very long time. If they are pee'd on and you have to remove the nest, always put a little bit of the old nest back (there's usually some dry even if slightly whiffy) and then put out a big pile of torn up strips of plain white toilet paper somewhere in the cage, so she can forage for it, pouch it and rebuild her nest. Likewise with the hoard, if you need to remove any, replace it with new food in exactly the same place.
5) House/nesting box - they need a house big enough to build a big nest in, that is dark inside so they can retreat to darkness when required. Also the nest needs to be big enough they can keep warm in winter. If they can't nest securely they will be stressed. Ideally a house should be open underneath and sat directly on top of the substrate - so they can do normal behaviours like burrow down to keep snug and bury hoards under the nest/in the house (so they can snack in the house).
6) Wheel - if the wheel - or anything else in the cage - is not right they will be stressed and try and let you know they are not happy with something (eg trying to escape!) For a Syrian, the wheel needs to be big enough that they can run with a straight back or it can cause back pain - most people get an 11" or 12" diameter wheel for a Syrian. The bigger the wheel, the easier they find it to run in too. Other little things like - if the food is on a shelf and the shelf isn't very accessible (eg ladder too steep or no ladder at all!) Or if everything is a bit empty in the cage and they feel too exposed and scared and don't have a dark place to retreat to.
7) Not enough food or water. Water bottles can empty themselves or stop working or be inaccessible - they need checking every day - sometimes it can help having two water bottles in case one fails. Food should always be available every day, even though they hoard most of it, there should always be food in the bowl each day.
So I would start with your hammy's environment in the cage. It may mean a cage upgrade, or a different house and/or wheel and possibly more substrate and bedding. Then maybe kind of start from scratch. Give her 2 or 3 days alone to adjust to the environment, explore and scent mark (they do this to find their way around by scent as they don't see well at all - so moving things or changing things mean they feel lost and confused). Then over a couple of weeks, don't clean or disturb anything and offer her treats through the bars and talk to her.
Then move onto handling and taming in a safe area like the dry bathtub or a playpen area. Unless she shows signs of wanting to come out before the end of the 2 weeks then that is ok too. The Ball can be useful for transporting them (ie carefully carrying the ball) to the bathtub and letting them out in there - with the odd toy in there. They then can't escape and you can gradually get used to stroking her (with gloves at first or use an old toothbrush so you're at arm's length) until she feels safer, gets used to your scent and trust builds.
Also when putting out the paper nesting material, you can put the toilet paper sheets up your sleeve against your skin for a couple of hours first, then tear it into strips and add it to the cage. The hamster takes the paper to the nest and it has your scent so it helps them become familiar with you.
She sounds a really livewire and a character! But biting and screeching is usually fear and stress. Taming can be time and patience, but when it happens it can be quite sudden and suddenly they are easy to handle and more affectionate