1. Flight. Literally. Like, on a plane.
2. TBD. Likely something like Islamic internment camps similar to the Japanese ones of the 40's
in the US. There are however a lot of other things that would also be big red flags
3. Lots of clothes and at least a few pairs of shoes. A laptop. All my HDD's.
4. Seeing as to how we're talking about an "oh shit" scenario many countries would likely allow Americans to gain citizenship through refugee status and living in said country for x number of years.
If you just need to get the hell out of dodge go to one of the "Schengen Area" countries: Austria, Belgium, Czech, Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland. As an American you can stay anywhere in that area for 90 days but it's all counted as one country in terms of that time limit. Once those 90 days are up you need to spend 90 days out of the area before you can come back. It's a max of 90 days in a 180 day period.
So once your 90 days are up you just need to go to one of the European countries that aren't in the Schengen Area: United Kingdom (England, Scotland, Wales, Northern Ireland) — 180 days, Republic of Ireland — 90 days, Romania — 90 day, Croatia — 90 days, Ukraine — 90 days.
I would, however, only use the above as a stop-gap for a longer termed solution: Enroll in a European university. Full-time foreign students are granted visas to complete their studies. There are many university courses taught completely in English throughout Europe (but your options will increase if you speak the local language). Additionally, a few countries charge foreign students the same tuition as its citizens — which can be as low as a few hundred euros a year. Once you have a visa, you are free to move around any EU country without hassle. It isn’t exactly uncommon for students to pay the super cheap tuition, get their student visa, and then just travel and never actually go to school.
There are many full-time foreign language courses in Europe that will enable you to get a student visa — this is a nice option if you want to learn a foreign language and travel on the weekends and holidays. These courses normally don’t follow the same tuition guidelines as normal European Universities, so they’re more expensive. For example, the intensive 25 hour/week French language course through the Sorbonne in Paris will cost about €2900 for a semester. However, student visa holders are often entitled to work part-time. There are many options available throughout Europe, but you’ll have to scour the web. The plus side to going that route is if you plan on eventually trying to live in one of those countries permanently then it's a good idea to learn the language anyways. It'll make it much easier to get a job, among other things.
As a worst case scenario, just enter the Schengen zone and overstay beyond the 90 days illegally. There are no border checks between the Schengen member countries. So if you were to travel from France to Germany nobody would look at your passport whether you're European or not. You should however avoid trains, because there are immigration officials on trains sometimes. Once you do decide to leave, if you've overstayed, don't leave from any of the Scandinavian countries, Germany, the Netherlands, Switzerland, or Poland because they're all pretty big on checking the length of time you've been in the area. France, Italy, and Greece seem to be the most relaxed with their immigration. They sometimes don’t even stamp passports of people entering on flights straight from the US. Additionally, they seem to never even look at the passports of outgoing travelers. Obviously, I would avoid doing any of the options in this paragraph unless it were indeed a worst case scenario. If you do take that route however, you might look into CouchSurfing.
I would however likely opt for somewhere like Svalbard
before resorting to the above paragraph, which I'd only do if enrolling in a European university fell through. The reason that enrolling in a European university would be my "go to" plan is because it's generally cheap and somewhat easy - some countries even supply you a stipend to live off of - and you're learning transferable skills once the shitfest ends. If you have to run away from the US for 4+ years then you may as well get another degree. Something you may have been interested in but never really had the time to go back to school for, or maybe try out a different career path you'd always considered instead of your current one. Or something more practical, like adding realistic skills to your chosen career path's resume - like additional more specialized degrees in your relevant field. At the very least just taking a full time language program would be useful if you do plan to reside in the host country permanently after the US goes to hell.