1. Do you recommend writing a book in chronological order, or just writing scenes and piecing them together as you go?
The first story I ever wrote was a bunch of different scenes stitched together. It ended up being four books long, which, when rewritten ended up being six books long. I've shelved it, but will be taking it out for yet another rewrite soon.
Many of my other stories were written in chronological order. Ethan Cadfael: The Battle Prince was written in an odd combination of both: it was composed of separate scenes which I wrote in chronological order then stitched together so that it flowed more cohesively.
The truth is, there is no right way or wrong way when it comes to the process of writing. There is only the way that works. What works for you might not be what works for me, or someone else. That doesn't make it wrong.
It may take you some practice and experimentation to figure out which way works best for you. Even then, it may change depending on you and the story you are writing.
2. Should I wait until I'm done my rough draft before I go back and rewrite older scenes, or is it a good idea to patch those up before I continue on?
I sometimes go back and do a very light edit on the scene I had written the previous day - a very light edit for spelling and grammar only. I do this to help get my mind back into the story so that I'm able to write the next scene without much struggle. That, however, is as far as I would go.
It is far too easy to get stuck in an editing loop and then never finish a manuscript. That helps no one, least of all yourself. If you find that something major in a some prior scene needs to be changed in order for the current direction your story to make sense, then make a brief note of it (the "comments" function in MS Word is great for this), then move on. You can, as they say, fix it in post.
Finish the manuscript; that is the important part.
3. And what are the pros/cons of self publishing? Does it work well?
Though I am self-published, I would like to also be traditionally published. The reasons for this are many and varied. First of all, there is that sense of validation that comes with a publishing contract. I'm not going to lie, that kind of validation is very attractive. There are other perks: I wouldn't have to pay to have a book cover done (which I usually do because I am bloody awful at book cover design). I wouldn't have to struggle with formatting the book, or pay someone to do it for me. They have professional editors that they pay to edit a manuscript. I wouldn't have to pay for such professional editing. The best part? They take care of the bulk of the marketing, something I am so incredibly awful at it's not even funny.
I hate marketing so much.
Traditional publishers also take care of the distribution of your books, and having a house behind your title opens doors that would otherwise be shut to you - many book reviewers refuse to take self-published titles into consideration, and it's far easier to get your titles into brick and mortar stores.
People also take you and your talent more seriously when you have a publishing house behind your title(s).
If you're self-published, you have to do all the work, and I mean all the work. You have to create your own cover, or pay out of pocket to have it done for you. The same with formatting. And editing. As for marketing, well, that's all on you all of it.
And there is so much about marketing to learn. So damned much. It's overwhelming. I don't do half the stuff I'm supposed to because I find it all so overwhelming even thinking about it gives me vertigo. That might be hyperbolic. The point is, it's a tonne of work.
Some writers, like myself, are not excellent marketers. We can write. That is the limit of our skills. Other writers are marketing whizzes, and they do everything with a breezy smile on their faces. I am not such a writer, though I wish I was.
The truth is, the pros and cons of self-publishing really do depend on the writer. I consider having to do everything a con, as I'm not good at it. I can write. That's all I'm good for. Others would consider that a pro. It does afford a level of creative control that is, if I'm honest, wonderful. And many people really enjoy the marketing side of things. Barf.
Truth be told, I really enjoy the process of self-publishing. It is expensive, however. While it is possible to self-publish and not spend a dime, if you want it done right, you're going to have to outsource your editing/formatting/book cover design, and that means money.
Once the book is published and out into the world, however? I really cannot handle the marketing side well. At all.
All I can say is do your research on the subject so that you can find which path is most comfortable for you. We are very fortunate to live in an age where we have these options, and we can make that decision. We writers are a varied bunch. One path won't fit everyone. Now it doesn't have to!