In many schools these days, it is SCHOOL (or district or school board or association) policy for students to have planners and for them to be signed daily by the parents. It was were I taught. (though I'm not teaching at the moment) I, as the teacher, was required by administration to check daily that those agendas were signed. I was REQUIRED to speak to the parents IN PERSON, if a student's agenda was not signed for even one day. Administration did spot check, and I would have been in trouble if I didn't. Your child's teacher may be in the same position. The agendas are fairly standard practice in most schools I'm familiar with. Most of my students used to leave their homework & agenda on the table/counter when they were done, and their parents would just initial when they got home.
Rubrics are a standard marking tool that have been around for decades and are used by every teacher I know. Teachers get tired of being yelled at for why little Tom, Dick or Harry got a B instead of the A that he deserves. Rubrics simply set out the criteria for marking the piece of work. I taught junior high, and I would give my students a copy of the rubric (and I would post one on the parents' message board outside my classroom door) when I gave out the project instructions so they would know exactly what they needed to do if they wanted an A. A rubric makes grading much more objective and makes it easy for anyone (other than the teacher) to see why the student got the grade they did. Again, school policy may drive this as well. I like rubrics and used from right from the day I started teaching, but I do know that several years into my teaching, the school I was in made it a requirement that teachers MUST use a rubric for any project.
While I'm not your child's teacher and I don't work in your school system, teachers DO have to meet the education requirements set out by the state/school board/province/whoever makes those decisions where you live. Teachers must meet those curriculum guidelines or objectives - whether they like it or not. Doing projects may be a part of that.
As someone who happens to be single and who taught, the implication in your post that single teachers don't care about their students lives and care about nothing except the 4 wall of their classroom I find quite offensive. Every teacher I know - single, married, childless, with children - DOES care about their students, both in and out of school.
And I have to ask - have you requested or had a meeting with your child's teacher(s) to discuss these issues? If not, you need to. Most of us are there to see children succeeding and would be really happy to work with the parents and make the accommodations necessary to see a student succeed. But teachers don't know if you have a problem if you don't tell them.
"Don't worry about the world coming to an end today. It is already tomorrow in Australia." Charles M. Schultz