She's 7 weeks old--far too young to be away from her mother. If outside of her crate, she will need to go out every 30 minutes at least. If she is inside her crate, she can hold it no longer than 2 hours.
Unfortunately, this is the reality of having a "cute little puppy." You won't sleep a full night for close to another month.
For the potty training:
-Keep working with the crate. Try keeping a log and note when she goes #1, #2, and when she eats. That way, you will start to develop an idea of her schedule and you will see that she needs to go out every 20 to 30 minutes for the first 2 weeks. Then, she will be reliable for no more than 30-40 minutes. However, as soon as you leave the room, she is free to go to the bathroom as much as she wants, even if only left for 5 minutes.
-Dachshunds are notoriously hard to potty train, but it is definitely possible. Each accident that she has, either in your house or in the crate, is a set back to her house training.
-Clean up all accidents with Nature's Miracle, Petastic, or other enzymatic cleaner than will eliminate the scent to her.
-Every accident that she has is your fault. She should NEVER be punished for your failure to recognize that she needs to go out.
Crate training:
-It isn't normal for her to hate the crate at all. She should love it! It is normal for her to hate being away from you, though.
-Her crate should not be used as punishment. It should have a soft blanket, some stuffed toys, a nylabone, and a t-shirt or something that smells like you.
-Each time she goes in her crate, praise her like she's the best dog in the world and give her a high value treat. (Nothing too big, her stomach can't handle very much)
-Never take her out of the crate while she is crying. If you do, you're just reinforcing the screaming and she will continue to do it every time she is in the crate (just to get your attention).
-Don't give her the chance to outsmart you, she's an infant puppy! Don't give her the choice of eating or not. Put her food in the crate, close the door, and wait for her to eat and then fall asleep. (Almost all puppies fall asleep right after eating. As soon as she wakes up, take her out)
-Like I said before, no more than 2 hours alone in the crate or she will have an accident. (Set an alarm if her crying doesn't wake you up.)
It sounds like a lot of work...and it is. You signed up for this when you bought a puppy--it is your obligation to put your life on hold while she is growing, sacrifice sleep, and be as consistent as possible with her training.