Slitherine

Can we assign an artillery support hero to a paratrooper unit ? If yes, how strong would that artillery be ? Like a 10 inch one ? How can we know ?

Yes, the AI has attached ArtSup to Aircraft. {Kerensky does the assigning for the AI].
Note: Paratroopers have low ammo so might make poor Art.
I don't think the SuppressingFire trait applies, so the supporting unit just fires first as if it were attacking.

Note 2: 10inches is 254mm, heavy cruiser class weapon.

I don't think we have any ground artillery units with a caliber larger than 8 inch yet (let's say the German 21cm is also 8 inch and forget their super heavy guns like Karl and Gustav) though.
Game status wise, infantry has no more than 13 SA, while the smallest 75mm arty has 12 SA with Suppressing Fire, of course, so it's a litter hard to compare them without a given target, as attack value have to be reduced by target Ground Defence first before calculating damage it can dealt, plus the accurancy and suppress/kill rate also changes with other traits and exp level.

Arty SA value just for comparison:
75mm (3 inch) class: 12
105mm (4 inch) class: 16
155mm (6 inch) class: 18
203mm (8 inch) class: 20

K5 (280mm (11 inch) : 24
Karl (600mm (24 inch) mortar) : 60
Gustav (800mm (32 inch) ): 82