First of all welcome to the forums 
Secondly Jax already told you which files belong to TTW so you can delete them so I don't need to say it again
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Thirdly to verify the cache in steam just open steam, click on the tab saying "Library" find the game you want to verify the cache for on the left side of the screen, right click on the name of the game and from the drop down menu choose "Properties" on the popup windows that appears click on the tab "Local Files" you will see four options and you will want the last one "Verify Integrity of Game Cache...". Hope this helps.
Now what I know about BSA patching problems is that they are usually because of the BSAopt software that is included with the installer, and windows xp, the BSAopt is third party software, it has nothing to do with TTW or is in any way related or associated with this project so we can't control that. Also IIRC it is the only BSA packer in existence so we can't really use a different one either
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Also remember this is a ALPHA version, and it is sure to have problems, there is nowhere else I can think of that would release an Alpha version of a software for public use, usually they release a Beta version and I must say that TTW is already more bug free and stable than many Beta version software out there, and Jax and Chuck are the main Devs of this project, other amazing people lend their help from time to time but pretty much of the vision and work on making this amazing project reality is of those two people that spend countless hours of their already busy days to bring us this awesome project (I call TTW a project and not a mod, because it is way more than just a mod) and what do they ask in return, nothing more than the users to enjoy their work, when a user can't enjoy it for some reason, they many times go out of their way to help and fix it. I don't understand what you mean about Jax and other people's tones in bug report posts, they are always helpful posts unless the person is asking for something that they already explained several times in different posts, and usually is them to say for that person to search the forums because their problem was already addressed and if it won't work for them then they should post on those other threads already made. Which in my opinion is the right thing to do.
Even though Jax didn't like your tone in your opening post, he still answered your question, I see no reason for you to continue ranting about him not liking your tone after that. Many people (thousands) got TTW, installed it and it worked out of the box using those instructions you complain about, instructions are made so people follow them and get it working, if by following the instructions a user didn't managed to get it working then there is a problem and it can be a huge amount of different reasons that is happening, that is why the user is asked to read the forums in search for a solution, if no solution is found then the user posts about it in a thread that is talking about the same problem and asks for help because the solution wasn't found, this doesn't seem unreasonable to me, it comes quite naturally to be honest.
I myself had problems installing TTW 2.2 it took me three days of constant installing, deleting, uninstalling, downloading C++, .NET, restarting the computer and it really frustrated me, I am the leading tester and I couldn't even install it while most users were already finding bugs I was supposed to find
then all of a sudden it just worked, there was no explanation, I still have no idea how it worked when it had failed so many times before (really many times), that is the way software is, moody...
A tip, when you have a problem and ask for help, there is a little thing called modesty, after all its all so easy to blame others for our own mistakes, I downloaded this, followed the instructions and it's not working, it must be the instructions fault, I just go to their site and tell them off and ask for help at the same time and not only that but I will also threat them that I will go on the site that suggested TTW and write bad things about it, lets be honest the team couldn't really be less impressed, they do this for fun not for money or fame, also if you do write about how awful people in this forum are please send me the link of that site and your post so I can laugh at how you make this site more popular (because people will want to come here and see for themselves the evil admins and mods, kinda like a zoo).
A second tip, grow up, if you think the world owes you everything when I doubt you gave anything to it than you're in for a tough reality check one of this days in your real life.
Hope you get your TTW working and can join the thousands of TTW happy "costumers"
and if you have any other questions feel free to ask, I am here to help. 