1a. My first job laid me off after 10 months, the CEO decided to relocate the company to the Caribbean for a tax break/shelter, which required hiring 70% local people. As the core company was small, the only people retained were the C-level, VPs, and their secretaries. Only 2 of 10 people from my office were retained (and forced to relocate).
1b. My Second job laid me off after 2 months. This small software company had split in two just before my arrival because the two lead programmers did not get along. I was placed with the disagreeable lead, who didn't want me on his team. When a newly degreed former employee, who left on good terms, stopped by one day looking for a job. My boss volunteered my position. The day before layoff I had talked to my leads boss about the good work I had been doing and the next project I would tackle, the next day they laid me off telling me they decided to go a different direction.
2. Yes, negatively. Both times.
3. Kinda some social stigma after the second layoff. I had relocated for both jobs, and didn't have a great support system either place. After the second layoff, recruiters/hiring managers treated me as I was the problem not just some misfortune.