What is the best approach when contacting a designer to avoid a negative answer?

If you can’t afford a good designer, you can’t afford a good designer.
Most designers I know of have a chip on their shoulder about being asked to work for too cheap, or worse, free. It shows a great disrespect for them as a person and for the work that they do.
A common mantra is “Work for Full Price or Free, Never Cheap.” Working for full-price should be obvious. Working for free has its benefits, and many designers will work for free if the project seems worthy or at least really good for the designer’s professional growth. Working for cheap devalues the profession and undermines the process, the results, and other professionals.
If you are somehow charitable or working for a good cause, maybe you can woo a designer or firm to work for free. If not, pay full price. The only way to get cheap is by luck; you won’t likely woo a designer (or doctor, or lawyer, or any other professional) into accepting less money than they are worth. You may get lucky and find someone who doesn’t know better though. …or a designer who’s just not worth very much (but then, their work probably isn’t either).
I can say that I am not at all intrigued by a website that has taken ten months to produce no results, no investors, a low budget, and an unfinished product that I’m not allowed to know about. At the very least you have to tell people what you do, or intend to do.
What are the best resources available online for learning design thinking?

Design can only be learned by doing.
The Stanford d.school has a Virtual Crash Course at http://dschool.stanford.e
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UPDATE 5/9/16: IDEO U has paid courses on ideou.com taught by some of their heavy hitters.
UPDATE 4/15: Coursera is currently running a class: “Design: Creation of Artifacts in Society” starting April 29, from Karl Ulrich at UPenn/Wharton. He’s also published a free e-book you can use with or without the course: http://ulrichbook.org
Also on Coursera: Human-Computer Interaction from Stanford’s Scott Klemmer, started March 31.The material is geared towards making user interfaces, but the design thinking process is simply a generalization of the design process, which Klemmer uses throughout in the context of UI. Recommended!
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After every project, no matter how small, ask yourself: “How did the process work for me? Where do I feel confident? Weak? Excited? Anxious?” Then iterate and improve yourself. Don’t judge yourself too harshly. If you aren’t failing, you aren’t doing it right. But remember: design is supposed to be playful and fun.
After that, try using the d.school “mixtapes” (more in-depth) http://dschool.stanford.e
Then study the Bootcamp Bootleg: http://dschool.stanford.e
Find someone else interested in learning with you, and use something like Edistorm to brainstorm with them, and Evernote to keep track of your interview notes and design insights and ideas.
Finally, find someone who can mentor you online. I don’t know of a comprehensive course, so the best option is to get someone with experience to coach you through it. [I just started doing this for a friend.]
And then… do a few more design projects! Get involved with OpenIDEO. Make boring things fun. Think big and start small. And let us know how it goes!
What are good resources to learn the basics of UX?

I’ll keep it simple:
Start with Design of Everyday Things by Don Norman. then Elements of User Experience by JJ Garrett, then Designing for Interaction by Dan Saffer, then Information Architecture for the World Wide Web, and finally Sketching User Experience by Bill Buxton. The path after those books can take you into a million possible directions, but starting there will give you the gravity leap into outer space that you need.
Next to all this is find a community and a mentor. You need the community to learn from through example and conversation and you need a mentor who can guide you individually.
Good luck.
Why is embedded help not popular?

I’m wondering why modern help systems are more passive than active? For example, each good guide through something look like this:
So why we don’t see this directly on website (service provider), but have to search for an…
UI/UX Design Patterns: What are good examples of registration flows that require a lot of info but manage to make it a painless experience?

When Twitter redesigned their sign up process with the goal of increasing user engagement, they actually added a screen / step. But, that actually helped them and they said the experienced a 29% increase in growth. It’s articulated very well in this article: http://www.lukew.com/ff/e
The key is to break up the sign up / process into logical steps for the user, keeping in mind that if you can show the user the result of their action, then they’re much more likely to keep going. People love feedback – show it to them.