In 2012 Marta was on 22nd place in ranking of women's names popularity. It's more popular in an younger part of society.
I personally know a few girls named Marta, so... Yeh, I think it's common.
If somebody is "w związku" with somebody it is always a romantic relationship. But you can also say "w związku z (czymś)" wich means "due to sth/because of sth".
Because it's a lot wider, it doesn't imply a romantic relationship. In the Polish sentence, they're dating. Or maybe married.
Classic translatorese, because Marta is Marta, not Martha. Translating someone's name without permission can be disrespectful, and if it is a company name it can be illegal because companies have to register all the forms of name they intend using.
The English sentence also has "Marta". "Martha" is just accepted.
Although yeah, it used to be "Martha" until recently.
Do people actually follow these rules about the names when they are speaking in everyday conversation?