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Regular expression match when specific digits AND words appear

I am quite new to regex, working on string verification where I want both conditions to be met. I am matching text containing 7digit numbers starting with 4 or 7 + string needs to contain one of the provided words.
What I managed so far:
\b((4|7)\d{6})\b|(\border|Order|Bestellung|bestellung|commande|Commande|ordine|Ordine|objednavku|Objednavku|objednavka|Objednavka)
Regex above correctly finds numbers but words are after OR statement which I would need to follow AND logic instead.
Could you please help me implement a change that would work as AND statement between digits and words?

You can use
(?s)^(?=.*\b(?:order|Order|Bestellung|bestellung|commande|Commande|ordine|Ordine|objednavku|Objednavku|objednavka|Objednavka)\b).*\b([47]\d{6})\b
If you can and want use a case insensitive matching with re.I, you can use
(?si)^(?=.*\b(?:order|bestellung|commande|ordine|objednavk[ua])\b).*\b([47]\d{6})\b
See the regex demo.
This matches
^ - start of string
(?=.*\b(?:order|Order|Bestellung|bestellung|commande|Commande|ordine|Ordine|objednavku|Objednavku|objednavka|Objednavka)\b) - a positive lookahead that matches any zero or more chars, as many as possible, up to any of the whole words listed in the group
.* - zero or more chars, as many as possible
\b([47]\d{6})\b - a 7-digit number as a whole word that starts with 4 or 7.
Do not forget to use a raw string literal to define a regex in Python code:
pattern = r'(?si)^(?=.*\b(?:order|bestellung|commande|ordine|objednavk[ua])\b).*\b([47]\d{6})\b'

By default, everything in regex is AND
if you do
abc,
it means "a" AND "b" AND "c"
so there is no need for an AND in regex
just remove the | between the numbers match and the words
\b(4|7)\d{6}(border|Order|Bestellung|bestellung|commande|Commande|ordine|Ordine|objednavku|Objednavku|objednavka|Objednavka)\b
I assume the backslash with the first word \border was a mistake.
This can match stuff like : "4958374border"

Regex python find uppercase names

I have a text file of the type:
[...speech...]
NAME_OF_SPEAKER_1: [...speech...]
NAME_OF_SPEAKER_2: [...speech...]
My aim is to isolate the speeches of the various speakers. They are clearly identified because the name of each speaker is always indicated in uppercase letters (name+surname). However, in the speeches there can be nouns (not people's names) which are in uppercase letter, but there is only one word that is actually long enough to give me issue (it has four letter, say it is 'ABCD'). I was thinking to identifiy the position of each speaker's name (I assume every name long at least 3 letters) with something like
re.search('[A-Z^(ABCD)]{3,}',text_to_search)
in order to exclude that specific (constant) word 'ABCD'. However, the command identifies that word instead of excluding it. Any ideas about how to overcome this problem?

In the pattern that you tried, you get partial matches, as there are no boundaries and [A-Z^(ABCD)]{3,} will match 3 or more times any of the listed characters.
A-Z will also match ABCD, so it could also be written as [A-Z^)(]{3,}
Instead of using the negated character class, you could assert that the word that consists only of uppercase chars A-Z does not contain ABCD using a negative lookahead (?!
\b(?![A-Z]*ABCD)[A-Z]{3,}\b
Regex demo
If the name should start with 3 uppercase char, and can contain also lowercase chars, an underscore or digits, you could add \w* after matching 3 uppercase chars:
\b(?![A-Z]*ABCD)[A-Z]{3}\w*\b
Regex demo

Square brackets [] match single characters, only. Also round brackets() inside of square brackets match single characters, only. That means:
[ABCD] and [(ABCD)] are the same as [A-D].
[^(ABCD)] matches any character, which is not one of A-D
I would try something different:
^[A-Z]*?: matches each word written in capital letters, which starts at the beginning of a line, and is followed by a colon

start with alphabet and finish with digits

I'd like to define a regular expression in python3 where I can extract words that starts with alphabets and finish with digits.
what I've been trying is r'^[a-z][A-Z].[0-9]$'
and didn't return any single word.

Use
r'\b[A-Za-z]\w*[0-9]\b'
See proof. This matches words that begin with a letter, have any word characters after, and end in a digit. Notice the word boundaries that match whole words.
As per the valuable comment below, consider an alternative:
r'\b[A-Za-z][A-Za-z0-9]*[0-9]\b'
The [A-Za-z0-9]* won't match underscores while \w will.

Extracting a section of a string using regex with repeating ending words

I am attempting to extract some some raw strings using re module in python. The end of a to-be-extracted section is identified by a repeating word (repeated multiple times), Current efforts always captures the last match of the repeating word. How can I modify this behavior?
A textfile has been extracted from a pdf. The entire PDF is stored as one string. A general formatting of the string is as below:
*"***Start of notes: Collection of alphanumeric words and characters EndofsectionTopic A: string of words Endofsection"*
The intended string to be captured is: "Collection of alphanumeric words and characters"
The attempted solution used in this situation was: "
re.compile(r"*{3}Start of notes:(.+)\sEndofsection")
This attempt tends to match the whole string rather than just "Collection of alphanumeric words and characters" as intended.
One possible approach is to split with Endofsection and then extract the string from the first section only - this works, but I was hoping to find a more elegant solution using re.compile.

Two problems in your regex,
You need to escape * as it is a meta character as \*
Second, you are using (.+) which is a greedy quantifier and will try matching as much as possible, but since you want the shortest match, you need to just change it to (.+?)
Fixing these two issues, gives you the correct intended match.
Regex Demo
Python code,
import re
s = "***Start of notes: Collection of alphanumeric words and characters EndofsectionTopic A: string of words Endofsection"
m = re.search(r'\*{3}Start of notes:(.+?)\sEndofsection', s)
if m:
print(m.group(1))
Prints,
Collection of alphanumeric words and characters

Consecutive uppercase letters regex

I'm trying to use Regular expressions to find three consecutive uppercase letters within a string.
I've tried using:
\b([A-Z]){3}\b
as my regex which works to an extent.
However this only returns strings by themselves. I also want it to find three consecutive uppercase letters nested within a string. i.e thisISAtest.

I wonder why you have those word boundaries in your regexp \b? Word boundaries ensure that an word character is followed by a non-word character (or vice versa). Those are what prevents thisISAtest from being matched. Remove them and you should be good!
([A-Z]){3}
Another thing is that I'm not sure why you're using a capture group. Are you extracting the last letter of the three uppercase letters? If not, you can simply use:
[A-Z]{3}
You don't necessarily need groups to use definite quantifiers. :)
EDIT: To prevent more consecutive uppercase letters, you can make use of negative lookarounds:
(?<![A-Z])[A-Z]{3}(?![A-Z])
(?<![A-Z]) makes sure there's no preceeding uppercase letter;
(?![A-Z]) makes sure there's no following uppercase letter.