Can I run these plumbing lines like this?
What is the total number of fixture units that you have on your 3" line?  The clean out is not necessary, provided you can access it from the roof or another clean out is further up line. additional venting is not necessary. From viewing your photos, I would call in a professional plumber and have the repair done correctly and have someone that can be called back if some thing goes wrong. One last bit of advice, contact your local authority and have them look at your sketches of what you are doing, this could be the best way to get the information that you are looking for.