Girl

Bismihi ta'ala

If you have your family's blessings, and she has her family's blessings, then you can commence with communicating with her, within the shar'i boundaries of course. That would be something positive, to get the know the person prior to the marriage ceremony. 

However, if it is away from parents knowing, and without any correct guidance, then you should not do that. A male/female going behind their parents' and secretly communicating with another person, wanting to supposedly marry them, is not at all advisable. 

Parents should never be the last to know. That is a very disloyal trait, and in most cases ends very bad. First step is to have family involved, and then everything will fall in place, in shaa Allah.

With prayers for your success.  

Bismihi ta'ala

In our Shari'ah, we do not have any prohibition or censuring of marriage of a Seyid/Seyidah to a non-Seyid/Seyidah. This is a cultural practice and personal preference of a parent. 

One must bear in mind though that if one is to marry a Seyid/Seyidah, they must stress on a higher level of honouring and respecting them, due to their lineage to Ahlul Bayt (a.s.). 

As this is a frequently asked question, please refer to other answers given on this:

Zaid Alsalami's response to Is a female Sayed allowed to marry a non-Sayed male? (al-islam.org)

And:

Zaid Alsalami's response to Is it true that Imam Khomeini's daughters are married to non-syed Muslims? (al-islam.org)

And Allah knows best.

Bismihi ta'ala

The statement "emotionally unstable" is very broad, and so it could be difficult to say whether it needs to be disclosed prior to a marriage proposal or not. 

If she has a chronic illness that would affect her spousal relationship, and impede in what people would see to be a healthy marriage, then it is best for her to be upfront about everything so she is not left with a broken heart or an early divorce. 

In general, it is always better to be direct and clear about one's mental state of being, and to mention what would be for or against them. 

Everyone is entitled to get married, even if they have certain challenges they are facing, and of course she can get married if she is emotionally unstable, but honesty is always going to work to everyone's advantage. 

Hopefully, with therapy and support of her family and loved ones she can overcome these emotional difficulties, and maybe marriage will secure her mental stability, in shaa Allah.

With prayers for your success.