1) Why is the name Sitikantha used?
Sitikantha is an eternal name of Lord Shiva because it is stated in Vedas. Vedas clearly call Lord Shiva as "Sitikanthaya Cha". And Vedas were before Samundra Manthan and also before fight of Shiva and Narayana (as told in Narayania). So, Sitikantha can mean whose throat is white due to using of ash in neck. And more importantly Sitikantha name is used in just beginning part of 5th Anuvaka of Sri Rudram (YajurVeda) where all specific names are used. The names from Bhava to Vyuptakesha are Specific names of Lord Shiva. They are used for other Gods only for the sake of completing Sahasranaamas. And Sitikantha name also exists between the specific name. So it is clear it is specific name.
नमो भवाय च रुद्राय च। नमश्शर्वाय च पशुपतये च।
नमो नीलग्रीवाय च शितिकण्ठाय च। नमः कपर्दिने च व्युप्तकेशाय च। नमस्सहस्राक्षाय च शतधन्वने च। नमो गिरिशाय च शिपिविष्टाय च। (YajurVeda 4.5.1)
Salutations to Him who is the source of all things (Bhava). And to Him who is the remover of all cries (Rudra). Salutations to the destroyer (Sarva) and to the protector of all beings in bondage (Pasupati). Salutations to Him whose throat is blue (Nilagriva) and whose throat is also white (Sitikantha). Salutations to Him of the matted locks (Kapardin), and to Him who is clean-shaven (Vyuptakesha). Salutations to Him who has a Thousand eyes and a hundred bows. Salutations to Him who dwells on the mount and who is in the form of Shipivista.
So, Sitikantha name can be used irrespective of any events.
2) Your other questions can be answered from the fact that Lord Shiva is married to Sati and Parvati multiple times as I discuss in my answer here.
केचद्वदन्ति तां ज्येष्ठां मध्यमां चापरे शिवाम् ।
सर्वानन्तरजां केचित्कल्पभेदात्त्रयं च सत् ।।
Some say that Shivă (Sati) was eldest of them all, some say she was middle one and some wise trear her as youngest of all. All three opinions are correct, because of difference of Kalpa.
And Parvati who was present during Sumbha Nisumbha Vadh is not same Parvati present today. She became Sati in Pitri Kalpa (previous kalpa) and again Parvati in Present kalpa and again married to Lord Shiva. I have explained it in detail in the same answer
So there are many Parvati and many Sati. Bhagvatam may be narrating event of any time among those many. So we need not to be surprised seeing the word Satipriya, Dakshyaani etc..
Even if we consider Bhagvatam is describing churning of ocean of Present Chakshusa Manvantara when Sati had already died and still why Sati priya, Dakshyaani words are used? We can solve it in this way:
When Devas go in refugee of Lord Shiva in S.B. 8.7.19 the words used are:
"arakṣyamāṇāḥ śaraṇaṁ sadāśivam "
Feeling unsheltered and very much afraid, they sought shelter of SadaShiva.
It uses the word Saranam SadaSivam ie. Refugee of SadaShiva.
So, Devas may actually have gone to that place where SadaShiva lives (not where Sri Parvati Pati lives).
Also the terms like "ParaBrahman", "Paramatma", "Bhutatma Bhuta Bhawana", "Ishworo Bandha Mokshoyo" etc.. are used which applies to SadaShiva rather than Sri Parvati Pati as he has birth through forehead of Brahma (although it may also be used for him).
And most importantly S.B. 8.7.29 states:
"O lord, the five important Vedic mantras are represented by your five faces, from which the thirty-eight most celebrated Vedic mantras have been generated. Your Lordship, being celebrated as Lord Śiva, is self-illuminated. You are directly situated as the supreme truth, known as Paramātmā."
Five face is the representation of SadaShiva. So it is likely that Devas are in front of SadaShiva. Sada Shiva is always with his consort Amba as represented collectively by the term Samba SadaShiva.
So the term Sati Priya, Dakshyaani may be used just as epithets only just as names of Lord Krishna are also used to glorify Lord Vishnu, In the same way Sri Parvati Pati is direct incarnation of Sri SadaShiva. So he can be denoted by using epithets or names of Sri ParvatiPati.
As there are many Parvati we can't answer when did Lord Shiva married Sri Parvati? However we can tell when did he married with Latest Parvati (who is incarnation of previous Parvati and Sati).
And as answered already from the Prabhasa Khanda of the Skanda Purana:
In this Varaha Kalpa, O goddess, you became Parvati obtained by Himavan through his penance, when the Chakshusha Manvantara has passed off. O beautiful lady, due to the anger of Daksha you had to be separated from me for the duration of a day of Brahma. Your span of life is the period of his six months.
So, she was either born close to the end of the Chakshusha Manvantara or the beginning of the Vaivasvata Manvantara.
However this doesn't make Sri Parvati youngest of the Gods we worship now. It is because there were many Parvati in past age before the birth of Present Parvati.