weighted average depending on category, ignoring blanks

Greetings friends,
I am working on a markbook to use for my classroom. I have attached an example copy of my markbook with no names or private data.

1) I want to have weighted averages of various subject categories that ignores blanks. I have projects listed in the first row, weights listed in the second row, category listed in the third row.
For example, I would like to be able to put for each project what strand it goes with (for English let's say reading, writing, listening, oral) along with a mark and a weight and for the weighted average to be prepared.

2) I would like a project to be counted in multiple strands if I type multiple letters (so if it is both a reading and writing project i could write rw, but if it was just writing i would write w).

3) I would like to be able to create an adjusted weighted average as well for the various subject categories, where the mark is lowered based on how much weight is incomplete or blank.
Let's say there are three listening projects. Each one is worth 1 weight. I only do two of them. I get 75% on both. My weighted average ignoring blanks would be 75%. But since I missed 33.3% of the projects of that category, I would like the mark to be adjusted downward by 6.66%. So my final mark would be 68.34%. However, I would only want it to do this if the mark isn't marked as "a" for absent. If I was absent for that one project, it would be excused and therefore my adjusted mark would still remain at 75%. Is this possible?

The current formula I use to calculate the average is as follows =SUM(IF(H4:N4>0,H2:N2*H4:N4))/SUM(IF(H4:N4>0,H2:N2)). This works, but has the problem that it doesn't take 0s into account, and I can't figure out how to also require it to look a the category so I'm not sure how to apply it to the various strands (reading, writing, listening, oral).

Thank you. I apologize if there are mistakes in formatting. I tried to follow the forum rules but please correct me as needed and I will try to make revisions.