On the subject of the bottom bracket popping, and your mention of finding metal in the grease.. perhaps what you need to do is take it all apart and really flush everything out. Remove ALL the grease to replace it later.

While you have it apart a better quality set of bearings might help a lot. I have noticed on low dollar bikes that sometimes the bearing balls have imperfections and a tiny imperfection there can be really noticeable. One case in particular I found three bearings with what looked for all the world like hair imprints in the surface and one with what looked like a rust bit or a casting bubble. Replacing with ball bearings that were smooth and spherical made a HUGE difference.

Because you found metal shavings be overly aggressive about cleaning and rinsing and rinsing again. Rinse the bearings and the races and the BB housing. You can use ethyl-methyl-bad-stuff-in-a-can or you can use Simple green and HOT water. If you use SG or any other detergent rinse again with clean HOT water and dry thoroughly.

Depending on the application I may rinse with alcohol or WD-40 (this is what WD is *supposed* to be used for, as a Water Displacer).

Then when you are sure everything is clean and there is not a single metal shaving left wash your hands (bearings can't be too clean) apply liberal amounts of grease and re-assemble.