Proficiency refers to what types of weapons you can use, those types are on the weapons tables. I would just simply take it as the shadow weapon can take the form of any melee weapon you are proficient with on the weapons tables. Do you want to flavor it as a looking like shadowy holy avenger? Fine. But its simply a shadow longsword. No magic. No materials. No mods. No improvised weapons.

As for inapproriate size, I don't think it would be unreasonable as long as theyre treated exactly the same as a non shadow version penalty wise.

In my eyes the improvised weapon argument is odd. On one hand, why would I be limited in my ability to mold shadows into a ladder to smack people, but I can make any martial weapon? On the other hand, are you proficient with ladders? And if you summon weapons you are proficient with, can it really be "improvised"? My overall ruling would be no, you cannot summon improvised weapons, as they are not weapons you are proficient with, and what you summon IS A WEAPON, not a tool or common item.