I am an American girl who has been teaching in Europe for the past year so I thought I'd offer my advice/experiences.
1)What certification programs will best help me be able to score a teaching job in Europe considering my situation at this time?
In general, any TEFL qualification will do as long as it is at least 120 hours and included 8-10 hours of supervised teaching experience. I took mine a year ago through http://www.teflworldwideprague.com
and loved the entire experience. The main things schools look for in teachers is a degree and a TEFL certificate.
2) If I can't take an on-site certification program at this time, is it likely that I will be able to find a job in Europe with an online or weekend/combo certification program?
The thing I found most helpful about taking it onsite is the extensive job guidance offered by my school, and being present to turn in my cv in person. Most schools in Europe will want you to be in the country already, so it is definitely best to take a course in the country you want to live in. That also increases the chance that your school will have contacts they can hook you up with. Connections are essential for obtaining legal work in countries that are starting to prefer already legal, EU citizens. I'm not saying it would be impossible to get a job if you take a course online or in the US, but it would certainly make it much harder and might limit you to Eastern Europe.
3) I have also heard that British English is preferred in Europe over American English. Is this true? And if so, could the fact that I am American hurt my chances of getting a teaching job?
That is sometimes the case but no common. It is really being an American citizen that hurts your chances because you are not EU, not because of your accent. That is why I recommend taking the course in the country you want to live in. I have no idea how I would've survived in Prague and found a job without the help of my language school.
That said, teaching and living in Prague has been an absolutely amazing, life changing experience! I've enjoyed every minute of it and wouldn't change it for anything. My school offers lifetime job guidance and I'm currently taking advantage of that as I'm considering moving to South America...I can't wait to begin my next adventure:)