do go and use the 11+ forum, it really is the only place to get all the advice you need.
Just to say again, the 11+ does not get you a place. You take the exam and get a pass mark, or get a ranking (so in our area the school has 150 places and you will be told you are number 210) Or you will be told you do not qualify (failed)
This just gives you the right to put the grammar school on your application form.
Then you have to fill in an application form. This is done with the LEA you live in, regardless of where the grammar school is.
You put down your schools in genuine order of your preference. So if you want the grammar school, but she has a low score/ranking, it is OK you can still put it down.
Then the other school eg your catchment school (do not assume that you are likely to get a place in any school, living in catchment doesn't guarantee you a place)
The way the system works is quite clever, it considers you for your first choice, and if you qualify, you get offered a place. If you do not qualify, your second school then moves up to first place and you are considered alongside the people who put it at number 1 so there is no disadvamtage to putting it second.
If your daughter has an advantage due to adoption, she still has to pass the exam, with a qualifying score. Then she will be higher up the list than a none LAC.
As to preparation, exam technique really helps, this includes things like
-if you can't answer a question, have a sensible guess and move on (or put a circle round it and come back to it)
-put and answer for every question, whne they say 1 minute left fill in the rest of the answer sheet
-use the multiple choice answers to help you, the answer has to be one of them
-practice filling in a sample answer sheet, noting if the answers run left to right or top to bottom etc.
-timing, keep an eye on the clock and how many you have done, don't spend too long on one question.
Make sure you have practised all the types of question, eg does she need to do NVR?
Free practice papers are available on line eg Bond, CGP
Lastly, make sure she knows her maths terminology, range/median/mode/mean/iscoceles/scalene/prime/factor/multiple.
Not difficult, but they use the correct terminology, and it is a shame to miss a maths question for the sake of a word.