I agree with Layna, toilet training and crate training are 2 different things.
A crate should be a sanctuary for your puppy, a place of safety, a place of her own where she/he can retreat safely, like a den in the wild.
There's several ways to train your puppy to use the crate but this is what I did:
First make it comfortable with blankets and old duvets. The crate needs to have a blanket over the top, like a roof to simulate den conditions.
You need to make the puppy understand the above by associating the crate with positive experiences.
Food is by far the best reward. Keep the crate open, and lure your puppy closer and closer. Eventually placing a treat in the crate. Repeat several times until the puppy feels comfortable or goes in on its own. A command can be added later. This may have to be repeated several times. If the puppy gets in the crate, getting hugs and fuss in the crate is really useful to emphasise security. I also used to feed my dog in it as well.
If you want to close the door, you can sit next to the crate when your puppy is in until they start sleeping and relaxing. Then I slowly closed the door and stayed there whilst reading, enhancing calmness. Did it several times a day till the closed door didn't bother the dog. Then I start on moving away, a few feet at the time, until I can do anything around the house.
Don't go too fast. Don't be afraid to go back a step.
The most effective training is for the puppy to work it out with your guidance.
Never force a dog to do something, crate should never be associated with negative experiences.
**ADDED ANSWER **
Walking your puppy at night might be detrimental to the aim you're trying to achieve: basically your puppy being able to hold it all night!
I understand it might be necessary but you should focus more about bladder emptying during the day. Dogs love routines, it makes them feel safe. If you organise a strong routine through the day, nights should get quickly sorted.
If a dog was wild, this would be a typical day:
Get up at dawn(birds usually give them the queue)
Out of the den to look for food. This can last all day if they're not good or very quickly if you have a clever one(which you do!). This is simulated by the walk! That's why you should always feed your dog after walking it.
If their belly is full, it's back to the den to sleep all day... or until they are hungry again.
Then back out again looking for food. Then back to the den.. and so on.
Then sleep all night, without need to go for a pee.
In all that, they empty their bladders as they look for food. You'll notice that an adult dog never empty its bladder in one go. What they do is leave little messages that they've been there, for others and for themselves for different purposes.
You need to get the puppy in a similar routine and wee training will work. Of course biology is a factor and she needs to grown in her bladder control, so be sensible.
I hope that helps. Focusing just on bladder control is not the exact answer, giving your puppy structure is.
Hope that helps. Good luck!