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Is it possible to have one regex that solves this task?

string = '1,23'
When a comma is present in the string, I want the regex to match the first digit (\n) after the comma e.g.2.
Sometimes the comma will not be there. When it's not present, I want the regex to match the first digit of the string e.g. 1.
Also, we can't reverse the order of the string to solve this task.
I am genuinely stuck. The only idea I had was prepending this: [,|nothing]. I tried '' to mean nothing but that didn't work.

You can match an optional sequence of chars other than a comma and then a comma at the start of a string, and then match and capture the digit with
/^(?:[^,]*,)?(\d)/
See the regex demo.
Details
^ - start of string
(?:[^,]*,)? - an optional sequence of
[^,]* - 0 any chars other than a comma
, - a comma
(\d) - Capturing group 1: any digit
See the JavaScript demo:
const strs = ['123', '1,23'];
const rx = /^(?:[^,]*,)?(\d)/;
for (const s of strs) {
const result = (s.match(rx) || ['',''])[1];
// Or, const result = s.match(rx)?.[1] || "";
console.log(s, '=>', result);
}

Find numbers that are in parentheses using regular expression and Javascript

There is such line
let str = 'ds 1,2abc{3,4}dd'
I need to find numbers that will be included in {} without enclosing the brackets themselves.
For example (Assuming that regex is a per-defined regular expression) I want to write something like the following.
(str.match(regexp)).join('').split(',')
Which will produce a result like this => ['3','4']
and if I have only one char in brackets or char with comma I need to get next result
let str = 'ds 1,2abc{3,}dd'
(str.match(regexp)).join('').split(',') => ['3','']
At the moment, I have such a regular const regexp = (/\d+\,\d*|(?<=\{)\d+/
but it does not handle the case when there are more numbers in the string with a comma like 1,2

It seems you are actually trying to include an empty string in your resulting array. Maybe you could use:
var str = 'ds 1,2abc{3,4}dd';
var res = str.split(/[{}]/)[1].split(",");
console.log(res)
var str = 'ds 1,2abc{3,}dd';
var res = str.split(/[{}]/)[1].split(",");
console.log(res)

The usual workaround, when the number of open/close curly braces is matching and you need not pre-validate your input, you may simply use
str.match(/\d+(?:\.\d+)?(?=[^{}]*})/g)
str.match(/\d*\.?\d+(?=[^{}]*})/g)
Here, \d+(?:\.\d+)?(?=[^{}]*}) matches 1+ digits, followed with an optional sequence of a dot and 1+ digits followed with 0 or more chars other than { and } and then a }.
See this demo
In a more generic case, you may extract groups of numbers inside curly braces by matching curly braces with comma-separated numbers in them first. Then, you may extract the numbers from each match:
const str = 'ds 1,2abc{3,4}dd{not this one 5,6} and {7,8.666,9,10.45}';
const rx = /{\d*\.?\d+(?:,\d*\.?\d+)*}/g;
const results = str.match(rx).map(x => x.replace(/[{}]+/g,'').split(','));
console.log( results );
See the regex demo.
{ - a { char
\d*\.?\d+ - 0 or more digits followed with an optional . and then 1+ digits
(?:,\d*\.?\d+)* - 0 or more repetitions of a comma followed with 0 or more digits followed with an optional . and then 1+ digits
} - a { char.

Javascript Regex: Capture between two asterisks with multiple asterisks in comma delimited string

I am trying to capture all characters between multiple instances of asterisks, which are comma delimited in a string. Here's an example of the string:
checkboxID0*,*checkboxID1*,&checkboxID2&,*checkboxID3*,!checkboxID4!,checkboxID5*
The caveat is that the phrase must start and end with an asterisk. I have been able to come close by using the following regex, however, it won't discard any matches when the captured string is missing the starting asterisk(*):
let str = "checkboxID0*,*checkboxID1*,&checkboxID2&,*checkboxID3*,!checkboxID4!,checkboxID5*"
const regex = /[^\,\*]+(?=\*)/gi;
var a = str.match(regex)
console.log(a) // answer should exclude checkboxID0 and checkboxID5
The answer returns the following, however, "checkboxID0 and checkboxID5" should be excluded as it doesn't start with an asterisk.
[
"checkboxID0",
"checkboxID1",
"checkboxID3",
"checkboxID5"
]
Thanks, in advance!

You need to use asterisks on both ends of the pattern and capture all 1 or more chars other than commas and asterisks in between:
/\*([^,*]+)\*/g
See the regex demo
Pattern details
\* - an asterisk
([^,*]+) - Capturing group 1: one or more chars other than , and *
\* - an asterisk
JS demo:
var regex = /\*([^,*]+)\*/g;
var str = "checkboxID0*,*checkboxID1*,&checkboxID2&,*checkboxID3*,!checkboxID4!,checkboxID5*";
var m, res = [];
while (m = regex.exec(str)) {
res.push(m[1]);
}
console.log(res);

Get the string between the last 2 / in regex in javascript

How can I get the strings between last 2 slashes in regex in javascript?
for example:
stackoverflow.com/questions/ask/index.html => "ask"
http://regexr.com/foo.html?q=bar => "regexr.com"
https://www.w3schools.com/icons/default.asp => "icons"

You can use /\/([^/]+)\/[^/]*$/; [^/]*$ matches everything after the last slash, \/([^/]+)\/ matches the last two slashes, then you can capture what is in between and extract it:
var samples = ["stackoverflow.com/questions/ask/index.html",
"http://regexr.com/foo.html?q=bar",
"https://www.w3schools.com/icons/default.asp"]
console.log(
samples.map(s => s.match(/\/([^/]+)\/[^/]*$/)[1])
)

You can solve this by using split().
let a = 'stackoverflow.com/questions/ask/index.html';
let b = 'http://regexr.com/foo.html?q=bar';
let c = 'https://www.w3schools.com/icons/default.asp';
a = a.split('/')
b = b.split('/')
c = c.split('/')
indexing after split()
console.log(a[a.length-2])
console.log(b[b.length-2])
console.log(c[c.length-2])
I personally do not recommend using regex. Because it is hard to maintain

I believe that will do:
[^\/]+(?=\/[^\/]*$)
[^\/]+ This matches all chars other than /. Putting this (?=\/[^\/]*$) in the sequence looks for the pattern that comes before the last /.
var urls = [
"stackoverflow.com/questions/ask/index.html",
"http://regexr.com/foo.html?q=bar",
"https://www.w3schools.com/icons/default.asp"
];
urls.forEach(url => console.log(url.match(/[^\/]+(?=\/[^\/]*$)/)[0]));

You can use (?=[^/]*\/[^/]*$)(.*?)(?=\/[^/]*$). You can test it here: https://www.regexpal.com/
The format of the regex is: (positive lookahead for second last slash)(.*?)(positive lookahead for last slash).
The (.*?) is a lazy match for what's between the slashes.
references:
Replace second to last "/" character in URL with a '#'
RegEx that will match the last occurrence of dot in a string

Filter not filtering from Regex

I am having having some trouble with a filter function that does not want to do what I need it to do.
I need this array to be filtered for strings within it that contain consecutive repeats of the same letter.
This is what I have:
var regex = /(.)\1+/g;
var filtered = permutations.filter(function(string){
return !string.match(regex);
});
Where permutations is equal to
["a,a,b", "a,a,b", "b,a,a", "a,b,a", "a,b,a", "b,a,a"]
The output for this just shows the same:
["a,a,b", "a,a,b", "b,a,a", "a,b,a", "a,b,a", "b,a,a"]
The output should be:
["a,b,a","a,b,a"]
Any idea what I am doing wrong?

It seems you need to match a repeated char after a comma, thus, change your pattern to
/(.),\1/
See the regex demo
Details:
(.) - Capturing group matching a single char other than a line break char
, - a comma
\1 - backreference to capture group 1.
var regex = /(.),\1/;
var permutations = ["a,a,b", "a,a,b", "b,a,a", "a,b,a", "a,b,a", "b,a,a"];
var filtered = permutations.filter(function(string){
return !regex.test(string);
});
console.log(filtered);