How do you know she is failing or missing assignments? Do you find them lying around the house? Did you get a progress report from the teachers saying "Missing 36 assignments" or are you tracking things on line. If the latter, do you have any idea how hard teachers work to do lesson plans and provide engaging lessons, and therefore might not have time to update every single kid's record showing whether they turned in each worksheet? Do you know what weight each teacher gives each assignment, vs. how they weight tests, class participation/discussion, and other factors? That's a question for the parent-teacher conference. Another question is, what is the purpose of homework? Is it busy work just to give each kid the exact same practice opportunities, and to give teachers more to do? Or is it to give some kids the opportunity to solidify their skills using different types of assignments? When I was teaching, I gave kids a lot of ways to succeed, and while I didn't want them to totally blow off every homework assignment, I had a number of strategies to help kids manage without every one (depending on their abilities on that particular task or unit). Perhaps your daughter's teachers know what they are doing? But you are entitled to ask whether her assignments are truly lacking (verify the 36 as an accurate count) and ask their recommendation on how hard you should push vs. letting natural consequences occur.
You let go this past grading period - which is basically September and October, right? So if she got straight As, how did this backfire and how is she failing. I think you had the right idea - to give her more control over her own work. But I wonder if you just did it to prove her wrong and show that you know the best way for a kid to be a good student? Maybe she rebelled and is trying to teach you a lesson. That's pretty common in adolescence in school and in other areas - the harder you push, the harder they push back. She will never learn life skills or how to advocate for herself if you ride herd on her all the time. She's 13. What's the worst that could happen if she got docked some points or had to stay after school for detention or extra help? She'll learn!
Colleges do NOT choose students solely based on grade point average! They want well-rounded kids with a wide variety of skills. And they also want students who can manage their own workload. They want independent and self-assured kids who can make all kinds of decisions (academic, social, and more) when there are no parents to supervise anything. The kids they don't want are those who are driven by parents to get everything done - and they don't want those parents calling all the time either! (I saw plenty of parents at college freshman orientation who were shocked when the provost and dean both said that the parenting was done, and it was time to back off and let the kids soar!)
There are many wonderful colleges, and there's a school for every kid. They look at grades, yes. But they really don't care about the first marking period, or the third, when a kid was 13. They just don't. They look at recommendations from teachers. They look at activities and leadership skills. They look at community involvement and social responsibility. There is no magic combination of clubs or sports or jobs that create the ideal student - there are lots of options and I suggest you start letting your child do a few things that interest her. Don't micromanage that. She also needs down time and social time with friends. Let her experiment. She's 13. My son didn't find his passion until midway through 9th grade - for him, it was track & field. He loved it, devoted himself to it, and learned a lot by being mentored and then mentoring others. He had a bunch of other activities, nothing as time consuming but enough to give him a wide range of interests and experiences that told the colleges he'd mesh well with challenges, different experiences and a wide range of students with various backgrounds and interests. He was accepted by some colleges that his higher-achieving, study-all-the-time, take-all-AP-classes friends did not. In fact, our neighbor had a miserable high school career with few activities and zero fun because he was "AP-all-the-way" for 4 years and as a result had book smarts and no social skills. He really struggled.
And how do colleges judge grades if they are "given away"? There are so many ways. One is by using standardizes tests (either the SAT or ACT - some kids excel in one and not the other). Those tests include reasoning skills, not just regurgitation of facts. Another way is that they know the individual high schools. They really do. They track prior students and believe me, if a particular district was turning out a high percentage of incompetent or ill-prepared students, there would be fewer acceptances. I'm sure your district prints a list of what schools the graduates get into - if it's a short list of low-end schools, then you might have a problem. But my guess is, that's not happening. When your daughter is in 10h and 11th grade, there will be parent/college nights to help you understand all this.
For now, I'd have some confidence in your child, keep her occupied with friends and activities so it's not all video games and isolation, but give her down time and a chance to learn to manage her own life and time. Let natural consequences start to rule the day. Otherwise, you and your daughter will be miserable until she's 18, she'll learn nothing without you standing over her, and you'll drive her away from you.