It looks like you have been working hard on this. Good job to get this far! It is much harder to work from scratch, than to build a kit, but you can learn a lot!
This site: http://golddredgervideo.com/kc0wox/ is probably your best resource. OM KC0WOX does a great job of explaining a lot about the kit and shows many measurements done with a homemade RF probe and also has a lot of videos of the various signals on an oscilloscope. I hope this can help you diagnose your trouble.
You used six 2n2018 for your HF amp, I assume you are using Farhan's schematic for that?
What diode are you asking about for the 1n4001.
I'm not sure that the ne602 has enough power to drive the final amp all by itself.
FT37-43 is just what you want for all the broadband transformers used in the radio. Do not use them for the final low pass filter -- you need powdered iron cores for that.
Your VFO and BFO signals should look clean like in the linked site's videos. Be sure to have your scope probe on the proper test point, and use a 10:1 probe if possible.
From your video, sometimes it seems like your scope has a problem as the signal is not blanking on the trace return? This can make good signals look bad.
Be sure when you are posting questions here, that you specificy where your test points are for your measurements. This can help us understand your questions and measurements better.
Mark -- N7EKU/VE3