Can the groom deliver khutbat an-nikaah and write his own marriage contract?

Saying khutbat an-nikaah before doing the
marriage contract is Sunnah, because of the report narrated by Ibn Mas‘ood
(may Allah be pleased with him), who said: The Messenger of Allah (blessings
and peace of Allah be upon him) taught us to say tashahhud in the prayer and
tashahhud in al-haajah…

Narrated by at-Tirmidhi (1105) and an-Nasaa’i
(3225). Classed as saheeh by al-Albaani in Mishkaat al-Masaabeeh, no.
3149 

See also the answer to question no.
88130 

Secondly: 

There is nothing wrong with the groom
himself doing that khutbah. 

Ibn Battaal (may Allah have mercy on him)
said: The majority of scholars regarded it as mustahabb to say this khutbah
in weddings. Maalik said: This is a long-established practice, and the
shorter it is the better. Ibn Habeeb said: They used to regard it as
mustahabb for the suitor to praise Allah and send blessings upon His
Prophet, then propose to the woman.

End quote from Sharh al-Bukhaari
(13/260) 

Ibn Qudaamah (may Allah have mercy on him)
said: It is mustahabb for the groom or someone else to give a speech before
the proposal and acceptance, then the marriage contract is done after that. 

It is mustahabb to recite the khutbah of
‘Abdullah ibn Mas‘ood, who said:

The Messenger of Allah (blessings and
peace of Allah be upon him) taught us say tashahhud in the prayer and
tashahhud in al-haajah …  

End quote from al-Mughni (7/62) 

As there is nothing wrong with the groom
himself delivering khutbat an-nikaah, similarly there is nothing wrong with
him directly addressing the guardian of the bride, so that the proposal and
acceptance are exchanged: the proposal from the guardian and the acceptance
from the groom. In fact this is the original format, and there is only a
need for someone to do the marriage contract or to prompt the words because
many people are ignorant of such matters and have little knowledge of the
Sunnah in this regard. 

As-Saawi (may Allah have mercy on him)
said: 

“It is recommended to give a speech” –
with a rhyme and rhythm to it, starting with praise of Allah and the twin
declaration of faith, including a verse in which there is the command to
fear Allah, and mention of the purpose of the occasion.

“when proposing” i.e., when proposing
marriage. 

There should be “another speech when doing
the marriage contract.” But the one who is to give the speech first when
proposing is the suitor, who should say, after praising Allah and reciting
the twin declaration of faith: To proceed: our aim is to join you and be
your in-laws and part of your family – or words to that effect. 

Then the guardian should say, after
praising Allah: To proceed: we have accepted you and your proposal, and have
accepted you as one of our family – or words to that effect. 

The one who should give the speech first
when doing the marriage contract is the guardian, who should say: To
proceed: I give my daughter [or the woman who appointed me as her proxy], So
and so [mentioning her by name] in marriage to you, in return for a mahr of
such and such. After that, the groom says: I have accepted your giving her
in marriage to me. The proxy of the groom says: I accept her marriage to the
one whose proxy I am. 

End quote from Haashiyat as-Saawi ‘ala
ash-Sharh as-Sagheer (2/338) 

With regard to writing the official
documents, the only purpose behind that is documenting what has happened and
guaranteeing people’s rights. Whoever does this registration of the
marriage, it does not matter, and that has no impact on the validity or
otherwise of the contract. 

For more information, please see the
answer to question no. 104662

And Allah knows best.