Well a friend of mine is Hanafi and he told me that abu Hanifa used to say that one should take any opportunity Allah gives you.
This would mean you can pray Dohr and Assr as Jama' (joined- at the same time but as two different prayers) and qassr (shortened) (Dohr if you are still in your city should be done normally 4 Raka' and Assr 2 raka') and either you try to keep wudu to pray Maghrib and Isha' or later Fajr (farida) also (if you won't have the possibility to pray one of them before their "Time" ends) or you do tayamum to pray as their is not enough water in the airplane.
Note that Hanafi scholars according this Arabic fatwa apparently reject joining two prayers (except for Hajj: in 'Arafah and al-Muzdalifah). On the other hand they consider qasr as wajib (while the majority consider it as jaa'iz/allowed), so according this one is not allowed to pray four rak'a while traveling and has to pray each prayer on time (see also this more detailed fatwa in Arabic), but they accept a "look alike joining" which means praying one prayer at the end of its time and the other at the beginning of its time.
I'd like to point at the fact that this is clearly contradicting the majority of scholars and even the prohibition of joining prayers is contradicting a sahih hadith.
About how you pray, I can only say: you can pray in your seat (prayer by Ima') and at least do the salam as usual. As you can do the prayer sitting (even if standing would be the best) according to for example the Verse 191 in Surat Aal I'mran (3:191)
who standing and sitting and lying down remember Allah and reflect
upon the (wonders) of the structure of earth and heavens. ..
And as mentioned in some Ahadith
Narrated Abdullah bin Buraida: 'Imran bin Husain had piles. Once
Abu Ma mar narrated from 'Imran bin Husain had said, "I asked the
Prophet (p.b.u.h) about the prayer of a person while sitting. He
said, 'It is better for one to pray standing; and whoever prays
sitting gets half the reward of that who prays while standing; and
whoever prays while Lying gets half the reward of that who prays
while sitting.' " Sahih al-Bukhari
Note that some madhhabs are very strict on this as they say if you are physically able to stand you should pray standing and consider a prayer to be void if you prayed while sitting, etc. I've even read fatwas obliging people to pray in the airplane floor while standing and making wudu' in the airplane toilet.
While for example in the Shafi'i and Hanbali maddhab they use soil (and seem only to accept this, note this is also the view of abu Yusuf the student of abu Hanifa) but according the Maliki and the main line of the Hanafi madhhab (this is also the view of ibn Hazm, al-Awza'y, a-Thawry, ibn Taymiyyah and a statement of Imam Ahmad) you can take a (small) stone with you and do tayamum with it (this would also be accepted by abu Hanifa himself and his student Muhammad ibn al-Hassan)!
Now an other point about the difference in some madhhbas is, that even if there are Ahadith which allow praying while riding (a horse, a donkey, etc. and according to that a plane, ship and maybe a car...) the consensus maybe about nafl (optional) prayers (as this is mentioned explicitly in some sane Hadith), but for fard (farz) some may say you should do the prayer again once you landed or you turned back to basement/ground.
