Hey op, when I was a young lad I had two studs break on the front of my integra. I used a drimmel tool to cut the backs down to get clearance to push them out. Then I cut a small angle on the back side of the new ones to fit them in. Never had an issue and pressing wheel bearings in and out is not easy even in a shop. Lots of cutting, heating, and beating involved. Good luck!
Looks like Brake fluid contamination. Is this a ford? I bet the caliper is seeping brake fluid. Check brake fluid level and see if the caliper is wet anywhere, specially more so on the back side