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javascript regular expression allow name with one space and special Alphabets

how to write regular expression allow name with one space and special Alphabets?
I tried with this [a-zA-Z]+(?:(?:\. |[' ])[a-zA-Z]+)* but not working for me,
example string Björk Guðmundsdóttir

You may try something along these lines:
^(?!.*[ ].*[ ])[ A-Za-zÀ-ÖØ-öø-ÿ]+$
The first negative lookahead asserts that we do not find two spaces in the name. This implies that at most one space is present (or no spaces at all). Then, we match any number of alphabets, with most accented letters included. Spaces can also be matched, but the lookahead would already ensure that at most one space can be present.
Demo

Use this one:
[a-zA-Z\u00C0-\u00ff]*[ ]{1}[a-zA-Z\u00C0-\u00ff]*
Answer from other question

Matching variable-term equations

I am trying to develop a regular expression to match the following equations:
(Price+10%+100+200)
(Price+20%+200)
(Price+30%)
(Price+100)
(Price-10%-100-200)
(Price-20%-200)
(Price-30%)
(Price-100)
My regex so far is...
/([(])+([P])+([r])+([i])+([c])+([e])+([+]|[-]){1}([\d])+([+]|[-])?([\d])+([%])?([)])/g
..., but it only matches the following equations:
(Price+100+10%)
(Price+100+100)
(Price+200)
(Price-100-10%)
(Price-100-100)
(Price-200)
Can someone help me understand how to make my pattern match the full set of equations provided?
Note: Parentheses and 'Price' are musts in the equations that the pattern must match.

Try this, which matches all the input strings provided in the question:
/\(Price([+-]\d+%?){1,3}\)/g
You can test it in a regex fiddle.
Things to note:
Only use parentheses where you want to group. Parentheses around single-possibility, fixed-quantity matches (e.g. ([P]) provide no value.
Use character classes (opened with [ and closed with ]) for multiple characters that can match at a position in the pattern (e.g. [+-]). Single-possibility character classes (e.g. [P]) similarly provide no value.
Yes, character classes (generally) implicitly escape regex special characters within them (e.g. ( in [(] vs. equivalent \( outside a character class), but to just escape regex special characters (i.e. to match them literally), you are better off not using a character class and just escaping them (e.g. \() – unless multiple characters should match at a position in the pattern (per the previous point to note).
The quantifier {1} is (almost) always useless: drop it.
The quantifier + means "one or more" as you probably know. However, in a series of cases where you used it (i.e. ([(])+([P])+([r])+([i])+([c])+([e])+), it would match many values that I doubt you expect (e.g. ((((((PPPrriiiicccceeeeee): basically, don't overuse it. Stop to consider whether you really want to match one or more of the character (class) or group to which + applies in the pattern.
To match a literal string without any regex special characters like Price, just use the literal string at the appropriate position in the pattern – e.g. Price in \(Price.

/\(Price[+-](\d)+(%)?([+-]\d+%?)?([+-]\d+%?)?\)/g
works on http://www.regexr.com/

/^[(Price]+\d+\d+([%]|[)])&/i
try at your own risk!

decoding a JS regular expression

I am going through some legacy code and I came across this regular express:
var REGEX_STRING_REGEXP = /^\/(.+)\/([a-z]*)$/;
I am slightly confused as to what this regular expression signifies.
I have so far concluded the following:
Begin with /
Then any character (numeric, alphabetic, symbols, spaces)
then a forward slash
End with alphabetic characters
Can someone advice?

You can use a tool like Regexper to visualise your regular expressions. If we pass your regular expression into Regexper, we'll be given the following visualisation:
Direct link to Regexper result.

regex: /^/(.+)/([a-z]*)$/
^ : anchor regex to start of line
(.+) : 1 or more instances of word characters, non-word characters, or digits
([a-z]*) : 0 or more instances of any single lowercase character a-z
$ : anchor regex to end of line
In summary, your regular expression is looking to match strings where it is the first forwardslash, then 1 or more instances of word characters, non-word characters, or digits followed, then another forwardslash, then 0 or more instances of any single lowercase character a-z. Lastly, since both (.+) and ([a-z]*) are surrounded in parenthesis, they will capture whatever matches when you use them to perform regular expression operations.
I would suggest going to rubular, placing the regex ^/(.+)/([a-z]*)$ in the top field and playing with example strings in the test string box to better understand what strings will fit within that regex. (/string/something for example will work with your regular expression).

Identifying special non alphanumeric characters in a string

Im working on a password validation that should only allow a-z 0-9 and these characters "!"#$%&'()*+,-./:;<=>?#[\]^_{|}~`
I tried using a regex but I'm not too good with them and I wasnt sure if this is even possible or if Im not escaping the correct characters.
var allowedCharacters = /^[A-Za-Z0-9!"#$%&'()*+,-.\/:;<=>?#[\\]^_`{|}~]+$/;
if (!s.value.match(allowedCharacters)){
displayIllegalTextError();
return false;
}

You need to place the dash at the start or end of the regex, or it will try to create a character range (,-.). Then, a-Z isn't a valid range, you probably meant a-z. Also, you need to escape the closing brackets:
/^[A-Za-z0-9!"#$%&'()*+,.\/:;<=>?#[\\\]^_`{|}~-]+$/

Looking over the ascii chart here I see your regex could be reduced to this character range:
/^[\x21-\x7e]+$/
If you just want to learn special behavior of character classes, you should read up
on it via regex basic tutorials.
Note that class behavior differs amongst the different flavors.

Simpler and more to the point using unicode: ^[\u0021-\u007E]+$.
/^[\u0021-\u007E]+$/.test('MyPassword!') // returns true
/^[\u0021-\u007E]+$/.test('MyPassword™') // returns false
Now if you would like to go a few steps further and actually create a more complex validation such as: minimum length 8 characters and at least one lowercase, one uppercase, one digit and one special character:
^(?=.*[a-z])(?=.*[A-Z])(?=.*[0-9])(?=.*[^a-zA-Z0-9])[\u0021-\u007E]{8,}$

Specifying complex conditions in regular expressions

The id attribute values in HTML 5 has the following rules
1.The string should contain nonwhitespace characters
2. It should contain at least one letter
How can i represent this in regular expression form.I reached in a regular expression which satisfies the first condition..
/(^|\s)\S+/ig
But how can i indicate the second condition in to the above regular expression
...and I am new to regular expressions...

You have got your restrictions wrong. The HTML5 ID data type must:
must be at least one character long
must not contain any space characters
That's:
^\S+$
Done.
Note:
Without any characters in your regex (\S is not a character), you don't have to make your regex case-insensitive (/.../i is superfluous).
Since your regex is anchored (^...$) there can only ever be a single match. This means there is no need for the "global" modifier, so /.../g is superfluous as well.

The easiest way would be to match on two expressions.
myString.match(/(^|\s)\S+/i) && myString.match(/[a-zA-Z]/)