Is CSS3 an Official Standard

When will CSS 3 and HTML 5 become the official standards?

i believe the official line is that it will be done when its done. theres a tremendous amount of work still left to do on it.

Is CSS3 part of HTML5?

HTML5 and CSS3 are completely separate things, so browser support for one does not always mean the other, especially considering that HTML5 is still a working draft (CSS3 is currently a recommendation).

That being said, with todays modern browsers, most will support the common HTML5 and CSS3 features. Internet Explorer 9 still requires a little help in regards to HTML5, you can use what is known as a HTML Shiv (or shim) to 'polyfill' support. Here is a guide to what IE9 supports: http://www.impressivewebs.com/html5-support-ie9/

Is there an “official”/standard CSS3 gradient syntax?

An update for 2011, the Mozilla syntax is now the 'official' one, adopted by the CSS3 Image Values and Replaced Content Working Draft. Webkit has been updated to use this syntax too, and this has now been incorporated into the latest versions of Chrome and Safari.

HTML(5) and CSS(3) Standard library / API?

The most official reference you will find for HTML is on w3 but it's honestly not that good. I can't even find the document for CSS.

HTML Reference on w3

I highly recommend using the documentation on MDN instead.

HTML docs on MDN

CSS docs on MDN

Why standard rule must be at last?

When writing CSS3 properties, the modern wisdom is to list the "real" property last and the vendor prefixes first:

.not-a-square {
  -webkit-border-radius: 10px;
  -moz-border-radius: 10px;
  border-radius: 10px;
}

Why is this method of ordering properties so commonly taught? Here is what it would look like "the wrong way":

.not-a-square {
  border-radius: 10px;
  -moz-border-radius: 10px;
  -webkit-border-radius: 10px;
}

Even doing it "the wrong way", won't the border radius be the same no matter what, forever? A quick investigation might lead you to conclude that it will, and this ordering of properties is rather nonsense.

The Long Long Ago: None of the properties are supported, order doesn't matter.
The Past: Only vendor prefixes are supported, order doesn't matter.
The Now: Both vendor prefixes and actual property are supported. If prefix is last, it will override actual property, but both are the same anyway.
The Future: Only actual property is supported, order doesn't matter.

More about

Is CSS3 fully enabled in every browser?

The CSS3 specification itself is incomplete, so it cannot possibly be "fully enabled" in any browser at the moment. It probably won't reach widespread standardization for another few years, especially given its granular modularization, but I suppose we're getting there.

If you need any sources from the past month, here you go:

How do I find out when I can safely drop vendor prefixes for a CSS3 property?
Do we have to use non-standard/browser specific CSS vendor prefixes anymore?

What are CSS3 Modules?

CSS level 2 is a monolithic specification. You have a single specification divided into sections, with each section describing a basic component of the CSS formatting model, for example:

Selectors
Cascading and inheritance
The box model
Colors and backgrounds
Fonts

The definitive CSS level 2 standard is CSS2.1, or CSS level 2 revision 1, which became a recommendation in 2011 following a set of changes to the 1998 standard for enhanced interoperability. The CSS2.1 specification can be found here (with the examples above linking to individual sections).

Post-CSS2 you have modules, which are basically various sections of CSS2 split into their own specifications. The above examples from CSS2 have the following corresponding modules:

Selectors
Cascading and inheritance
The box model
Colors and backgrounds (yes, that's one section split into two modules)
Fonts

This means you have multiple specifications that all pertain to CSS, each with its own independent development path. This consequently means that different modules can progress toward implementation and standardization at different rates, without having to depend on the rest of CSS as a language (which was the primary cause of CSS2.1 taking so long to become a recommendation following CSS2's standardization). These specifications are collectively known as CSS3, or "CSS level 3", although each goes through levels on its own, making it somewhat of a misnomer.

CSS3 and its modularization system are explained in greater detail in this other answer.

CSS3 lines without using images

try

div {
  width:50px;
  border-right:1px solid black;
  box-shadow: rgba(255,255,255,0.8) 1px 0px 0px;
}