Act 1 - Scene 5

First of all, I think that Rita won't go to the pub with Frank simply because he asks her to go in order to talk about her husband and as Rita doesn't want to talk about him she wants to stay in his office for Frank to explain her why Chekhov is a comic genius. Then, when Rita asks him to go with her to the theatre he first says no because he excuses himself by saying that he doesn't like theatres and that the production is played by amateurs. However, we come to know that the true reason has nothing to do with him liking theatres or not because he says that he can't go with her for Julia would be jealous if he does so. When Rita says 'what's she got to be jealous of me for? I'm not gonna try and rape you' and he answers 'what an awful pity. You could have made theatre exciting for me again' we come to learn that Frank feels some sort of attraction for Rita. 'If she knew (Julia) I was at the theatre with an irresistible thing like you.' If this is not obvious enough for me to say that he finds her attractive, I don't know what else do you want him to say! :P

Act 1 - Scenes 3 & 4

First of all, regarding Rita's view upon working-class culture I have to say that, although I agree with her on most of her ideas, I don't think that the working class has no culture at all. Of course that for deciding whether they have or not one I should first of all provide a definition for culture, so let's say that in this context, for me, culture entails everything that may result from the relationship and the exchanging obtained through the co-existence of people (language, behaviour, customs, habits, likes, dislikes, conflicts...). Considering this definition of culture, working class people do have their own culture. However, I do agree with Rita when she says that she sees 'everyone trying to ger from one day to the next,' she finds no meaning in this sort of life as they find themselves not living but surviving. She finds a very good way of explaining herself and showing what she means when she says that they have no culture. She gives the example of the Daily Mirror, The Sun and ITV bombarding people with ads for having them wanting more and more money to buy more and more things that they don't actually need but with which they try to convince themselves that they are happy when they are not...I found it really interesting when she says 'and the papers tell them what to spend the money on so the desease is always covered up.' (These absence of meaning, thoughts, beliefs, ideas and values in their lives is what Rita calls the desease)
Secondly, as regards what Rita learns by the end of these two scenes, I think that she learns to make connections. In fact, what she learns is the fact that she is perfectly able to make connections between many different things (her dresses, ITV, the Daily Mirror, addicts, her and her husband), and, as result of becoming aware of this, she will be able to start making connections for writing her essays.
Thridly, in my opinion, what is wrong with her essays is the fact that not only they are too short but they are also written quoting authors/writers that are not exactly writers of literature (here is when Rita learns that not every book is literature). However, I think that there is something more important that the mere fact that she's written them in this way: she hasn't taken enough time to prepare them, and here in when Frank learns more about Rita's life and her husband. He seems to be rather concerned about Rita's having to write her essays at home because of her husband's not allowing her to do it at home. This situation shows us more about Rita and her convictions: 'art and literature feed me inside... and Denny hates me comin' here. It's like drug addicts, they hate it when one of them tries to break away.' She knows that she is trying to break away, she is trying to break away from the meaningless and empty life that her husband is (and she was) living...
Finally, I think that Rita says that 'it makes me stronger coming here' simply because by doing so she is trying and fighting to get the life she wants for her...'I don't see any culture, I just see everyone pissed, or on Valium, trying to get from one day to the next. There's no meaning...' She is perfectly aware of what is going on with them and that's why she wants to do something. She wants to give herself the chance of breaking away and being different from those people (like her husband) that pretend to ignore what's going on, to ignore the desease.

'I just see everyone pissed, trying to get from one day to the next...Cos there's no meaning!'

Act 1 - Scene 2

As the story develops, we come to know more about both Rita and Frank. She finds it very difficult to leave behind her previous experiences in life in order to be able to be 'educated' by Frank. That's why she has problems with her first essay. She (as many of us most of the times) cannot 'criticise' Howards End without feeling discouraged by the author's opinion ('We are not concerned with the poor'). However, Frank finds the way to show (teach) Rita that we may not always agree with what we read (or with what we are faced in life) and, all the same, we will be always able to take something good from it (there are people with whom we agree and people who does not agree with us). I really believe that Frank is trying to show her that we have to be respectful upon others, their views and values...However, it is true that Rita may not be ready to accept this diversity yet, but I do believe that she will learn it sooner or later. We just have to give her more time! Because we can be sure that she'll be able to do it!

'Is this the absolute maximum I
can expect from this livin' lark?'
Rita

Regarding what Rita thinks about the proper students I would say that she thinks so simply because they are the ones that 'come here all time', she seems to have the 'typical' and 'ordinary' view of what a student is, i.e. students are the one that go to school. Consequently, Rita does not see herself as a proper student simply because she does not go to school. So, it doesn't matter if she is studying or learning she won't be a proper student as she does not go to school.
Finally, regarding Rita's opinion about Frank's room, I think that she just likes it. She said that although it's a mess, it's a perfect one. I think that Frank's description is great 'I just moved in. The rest sort of happened.' What Rita likes is the fact that he has not even taken a moment for arranging it. 'It's like wherever you've put something down it's grown to fit there.'