It really can not work that way:
- What should I do now?
- Kiss her.
- OK, I will...
...
- I kissed her. What should I do next?
Neither that nor learning all you should do and try to apply it in reality...
I'll compare it to the chess game, you cant learn 5 moves and play them later, because it depends on your opponent too, what he will play and there are thousands of possible combinations. But instead you learn how to play, you acquire* (not sure if the word is correct) certain way of behaving, attitude, thinking. You learn the rules, and here, they are simple, "LEAD". You play the game, she follows. Sometimes with resistance.
Considering tactics, these guys are far better than me, I don't know why they (or anyone else) do not reply anymore... I think they think they have said enough, but it's just obvious that you need more detailed help. But don't expect that someone will give you a formula, and following it you'll win this girl.
Have that attitude - be in charge... You decide what to do, when, how. Of course not in a dictatorship way (they hate a slightest sign of domination [social, not sexual

]), but you will see, she will follow if she's interested.
Only friends work this way:
You: What do you think, we could do it / go there?
Her: Yeah, I think we could (or no...)
YOU DO NOT ASK FOR HER PERMISSION.
You decide what's best. If she really (I mean REALLY) can't do that, she will say it.
Quote:
I am not sure yet how I should proceed but I will try to get her for a walk tomorrow and just go for the kiss at some moment.
I think you should invite her at your place (alone of course

), and not for a walk, but I'm telling you here what the guys above have already told.
If it's awkward now, then you should create the situation and SPAM or reason for her to come. Not necessarily in a day, it might take more days to do it.
Quote:
What should I say if she brings in our last discussion ? Should I try to just make fun a little? Like "You're still thinking at those childish things?"
When you ask like that it shows that you really do not get the idea... If I tell you "yes", there still could be something more she would say afterwards and you wouldn't know how to proceed...
The thing is - WHAT SHE SAYS DOES NOT MATTER. This is maybe not the best explanation for you, but I just don't find words. The guy above has told you already like "talk, talk, talk..."
Maybe better explanation would be that YOU DO NOT TAKE HER SERIOUSLY, not like a human being, BUT LIKE A WOMAN.
Example:
She insults you and you get that angry that you attack her. This means you take her seriously and you FAIL LIKE A MAN, and not only in her eyes. But if you find a nice way to deal with it with dignity and still do not ruin or end the relationship, then you did it right (watch romance movies hahaha there you could find an answer - joking of course). It can be playfully, or any other normal way you can think up, it's up to you.
This would be a principle (not giving much value to what she says or does), like learning chess. Inside that principle you play the best you know. And playfully and smiling could be the best way, but after all that... you stay in charge... When I say smiling it does not mean smiling like a loser that does not know what to say... It means like you're looking at an angry child...
Now I'm starting to sound stupid but I'm trying to explain psychological things in a foreign language for me.

Don't do this to me man, take the responsibility, do something, try to learn the principle and move inside its borders...
Though this I quoted you might be OK to say, but here I'm trying to explain you your mood, not what you should say...
N I'm still there if you need help, but I think you should get the idea now...

n I hope there will show up more guys. "Two heads are smarter than one". Hahaha, expression in my language meaning two persons, not what one might think...
Edit:
I saw it only now...
Quote:
If I invite her to my apartment maybe she'll ask to bring some friends which I can refuse but it might scare her again
Don't refuse them directly. You might say like: "I would like us to be alone, I'd like that we talk / have dinner / watch movie", think up something, I'm sure you'll manage it, better than me (my suggestions).
Good luck! or better "Good knowledge !!!"