1. Women men cannot propose to

2. The women that men cannot propose to
Every women that one is not allowed to get married to temporarily or permanently he is not allowed to propose to.
Close relatives due to blood relations
Close relatives due to marital relations
Close relatives due to milk relations
Certain women due to certain cases

3. Proposing to women due to waiting period
Asking for a widowed women’s hand in marriage during her waiting period is allowed only if it is not explicit proposal, but figurative.
ولا جناح عليكم فيما عرضتم به من خطبة النساء (البقرة 235)
Explicit such as saying: I am interested in you
Figurative: you are a pious women, many would be interested in you.
As for women that have been divorced the third divorce, some scholars have said she takes the same ruling as the widowed.
Women that are in the second or first revocable divorce do not take the same ruling. As long as their waiting period has not finished, she is still considered married.
قال ابن تيمية: من خطب امرأة في عدتها يستحق العقوبة التي تردعه وأمثاله عن ذلك، فيعاقب الخاطب والمخطوبة جميعاً، ويزجر عن التزويج بها، معاقبة له بنقيض قصده»

4. It is impermissible to propose to an engaged women
In hadith narrated by Bukhari and Muslim: the prophet peace be upon him said: and no man shall propose over his brother’s proposal.
Albukhari added: unless he gets married or lets go.
في الصحيحين عن أبي هريرة رضي الله عنه أن النبي صلى الله عليه وسلم قال: لا يخطب الرجل على خطبة أخيه
زاد البخاري: حتى ينكح أو يترك
روى البخاري عن ابن عمر: نهى النبي صلى الله عليه وسلم أن يبيع بعضهم على بعض، ولا يخطب الرجل على خطبة أخيه، حتى يترك الخاطب أويأذن له»

5. Wisdom behind not allowing proposal over someone else’s
فلا تزكوا أنفسكم هو أعلم بمن اتقى (النجم 32)
ولا يغتب بعضكم بعضا (الحجرات 12)
Enhances animosity, greed, gossip, plots, and self praise between the members of the society.
ولا تعتدوا إن الله لا يحب المعتدين (البقرة 190)
والذي يؤذون المؤمنين والمؤمنات بغير ما اكتسبوا فقد احتملوا بهتاناً وإثماً مبيناً» (الأحزاب 58)

6. So what happens in case someone does get married to a women that was already engaged?
Scholars have different opinions
The marriage is invalid as mentioned by Malik, Ahmad
The marriage is valid, as mentioned by Abu Hanifa, Alshaf’ee, Ahmad
But all scholars agreed that the action in itself is forbidden and he and she will be sinned for it.

7. So do we separate between the new married couple, if the girl was engaged to someone else?
Scholars had different opinions
To be separated فسخ
Not to be separated
They would be separated, if no intercourse had taken place.
Preponderant ruling:
The marriage is valid, and we do not separate between them, but they are it sin for not leaving the promise of engagement. He would be holding a punishment of تعزير such as تأديب discipline, wish maybe such as a certain fine or what the judge sees a fair and reasonable compensation and punishment.
The reason why the marriage is valid, is because the way that he did it was not appropriate, but the contract was totally complete.

8. When is the women considered engaged
When is the women considered engaged? Therefore, cannot marry until she would break up the engagement?
A woman is considered engaged once her waliy (guardian) gives the consent that they are promising to continue the marriage in the future, whether a verbal consent or figurative consent.
She is not considered engaged for the proposal itself. (A common misunderstanding)
Evidence to that is:
فاطمة بنت قيس أخبرت الرسول صلى الله عليه وسلم أن معاوية وأباجهم خطباها، فأمرها الرسول صلى الله عليه وسلم أن تنكح أسامة»
Fatima bint Qays was proposed to by Mu’awiya, and Abu Jahm, but he peace be upon advised her to get married to Osama Ibn Zayd.