A beard is the unshaven hair that grows on the chin, upper lip, cheeks and neck of humans and some non-human animals. In humans, usually only pubescent or adult males are able to grow beards. Some women with hirsutism, a hormonal condition of excessive hairiness, may develop a beard.
Yes, it is permissible, and horse hair is tahir, so there will be no problem with that.
And Allah knows best.
In Islam, a man should groom himself and look nice for his wife.
It is related from Imam Rida (A): "The women of Bani Israel deviated from the path of chastity because their men were not bothered about cleanliness and looking nice." The Imam then added: "What you expect of your wife, she expects the same from you."
It is also related that Allah is beautiful and loves beauty, and loves to see the signs of His blessings on His servants.
The Prophet (S) used to give attention to looking appropriate and presentable. Here are some narrations on some of his grooming habits, including combing and oiling his hair and beard: https://www.al-islam.org/sunan-nabi-sayyid-muhammad-husayn-tabatabai/cha...
Of course, different people have different levels of motivation and interest in these things, and different understandings of what it means to be tidy.
So yes, you can ask, and yes he should make some efforts. Even if it were not emphasized in Islam, it is still good to try to accomodate one's spouse's requests as long as they are ethical and doable. However, it is difficult to force someone to change.
Perhaps you can encourage him, if you have not already, by giving him some nice beard oil. There are also some websites dedicated to beards and men who are proud of their beards. After all, a beard is a symbol of a manly man (for men who can grow them, of course) and so it is nice if he takes pride in it.
Also since the beard is symbolic of Islam, it is nice to look after one's beard because it is part of the public image of Islam.
Don't shave whatever you have on your face, even if it does make a full beard. Just keep it or trim it but don't shave it fully.
It depends on your Taqleed. Ayatullah Khoei allowed this small beard, but Ayatullah Sistani did not.
Moustaches is not part of beard .
Yes, as far as the remaining hair can be called by common people as a beard.
The minimum length of the beard is what can be seen as hair on the face by people who see you from usual distance of conversation, no matter how short it might be.
Yes it is not only allowed but even recommended (Mustahab) to dye the gray beard and gray hair with any color which suits you. Some non Shia Shaikhs claim that black color should not be used. This claim is not authentic and has no evidence. According to authentic Hadeeths, using any color which suits you is allowed.
Obligatory precaution means you Must act upon it or refer to the second most knowledgeable Marja' who has a verdict in this matter.
Applying any material on the skin or scalp is allowed even if it is Najis material as far as you clean the area before performing Wudhu or Salaah. Synthetic alcohol is not Najis according to many Maraaje'. Some scholars say that any intoxicant alcohol is Najis. Nevertheless, whether it is Najis or not Najis, it is allowed to apply it on the body or scalp.
It is not permissible for a man to only have beard in his chin as it implies "shaving" which is considered haram. As far as the trimming, the Muslim person should be considered as "having beard" according to common view.
With prayers for your success.
Keeping the beard for Muslim men is considered both a prophetic sunna and a wajib act. According to a widely-reported hadith the Prophet said: "Let the beard grow and trim the mustaches". Other traditions bring similar meanings too. Shaving the beard with no valid reasons, like medical necessity or coercion, is therefore considered haram. Some mujtahids have said that beard should not be shaved as "ihtiyat wujubi" (obligatory precaution) which substantially does not much differ from a clear prohibition.
With prayers for your success.
The growth of the beard that you described (covering the chin) is sufficient. Having the full beard is not wajib. Also, please note that on Shar'i issues, one has to fulfill what is incumbent even if the parents object to it.