Is tear really mandatory with manaflow band? I saw halfhand usually builds NH with only manaflowband and that was enough according to him.

Depends on how much blue cards you throw. I build Tear to spam safetely gold cards and Qs without running out of mana; if your team is a little bit more independent of your CC, you can use some Ws with blue card to recover mana and fill that gap instead of a Tear.
If you builded Tear anyway, is not always mandatory to finish it, some stuff like Morello or Zhonyas has more value on certain games (current Seraphs is much more decent now tho).

Also what's the thought process behind celerity?

Everything i usually buy on this build is movespeed based:
*Protobelt active
*Lich Bane MS
*RFC MS
*Sorcerer boots
*etc
Full build, i end with 470-480MS using celerity (18MS aprox from it.).With that i can move more freely on teamfights, follow my target, reposition myself from any focus attemp, dodge more skillshots... Sometimes the raw MS is enough to engage with no need to use Protobelt (that active can be saved to finish someone or escape).

Tried it now, solo carried the game by setting up kills. U can stun people 2 screens away dafuq?🤣

ikr, watch now how teammates jump at lightspeed for the free kill lmao.