Pygmalion Part 1

The thing that most interests me about this story is that it's not a novel. It's a play. You can immediately tell when it is seperated into Acts and not chapters. After I made this observation, I was curious about the Flower Girls lines. Since this is a play, it has to have been performed before. Does that mean that whoever played the Flower Girl had to talk like her during the play? For example, one of her first lines in the play is, "Ow, eez ye-ooa san, is e? Wal, fewd dan y' de-ooty bawmz a mather should, eed now bettern to spawl a pore gel's flahrzn than ran awy atbaht pyin. Will ye-oo py me f'them?"
This line makes no sense and I don't see how someone could read it, let alone memorize it. So, if the actress did have to talk like that, did she eventually switch to normal english soon after like they did in the written version. It would be much easier for the audience to understand, but how would they explain the switch? Would they have someone read the apology that is written in this version? I feel like that would make the play slightly confusing because maybe the audience would think the person apologizing is another character. This would make the story harder to understand.
Next, why do we not learn the Flower Girl's name until she goes to Higgins' home? Why is it that no one asks what her name is when she's trying to sell them flowers? That seems very peculiar to me. Another thing happens when she goes to Higgins' home. Her father shows up. At the beginning when she is trying to sell flowers, she made it seem like her father neglected her and that's why she's out on her own. So why has he taken sudden interest in her? I guess because he saw her as a way to get money because he ended up asking for some from Higgins. In which case I don't understand why Higgins would actually give him the money. If anything, Higgins should ask for money from Doolittle because he's the one teaching the girl. People usually have to pay for private lessons.