Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Yes, Nikah will be valid if the boy and girl are both sane, mature and had met the conditions of Kafaa'at or else the parents/guardian will have the right to nullify the marriage. However, the guardian/parents being present is Mustahab (preferable). (Hidayah Vol.2 Pg. 313, Badai'i us Sana'i Vol.2 Pg. 248, Ahsanul Fatawaa Vol. 5 Pg. 96)
In the case of 2 females and 1 man witness, the Nikah is still valid.
Allah Ta'ala says, "And get two witnesses out of your own men. And if there are not two men (available), then a man and two women, such as you agree for witnesses, so that if one of them (two women) errs, the other can remind her." (Surah Number: 2, Ayah Number: 282)
(Fathul Qadeer Vol.3 Pg. 110 and Vol. 6 Pg.45)
The wisdom for having witnesses for Nikah (marriage) and to announce it:
All the prophets (AS) and religious leaders are agreed that the marriage must be announced so that everyone may distinguish between it and adultery. So, the witnesses are appointed and it is reasonable that it should be further publicized through Walimah. People should be invited to it and it should be made known so that other people may learn of it and that there should be no misgiving later on. (The Wisdom Behind The Commands Of Islam, By Moulana Ashraf Ali Thanwi (RH)- Pg, 228)
The Khutbah is not a prerequisite for the validity of the Nikah. Khutbah is a Mustahab act of Nikah.