[RPG] Does picking up an item while under the effects of the Invisibility spell turn it invisible

It'worthless.

Summoning spells have the effect of bringing creatures (or objects) in your presence (and often of giving command over them):

A summoning spell instantly brings a creature or object to a place you designate. When the spell ends or is dispelled, a summoned creature is instantly sent back to where it came from.

Both these effects are already invisibly so the feat is useless. The creature himself isn't a creation of the spell so is unaffected by the feat.

The feat mainly speak about 'visual manifestation' of the spell while the Effect line of the spell is a technical term to indicate what the spell summon, not what is the effect of the spell. The effect of the spell is teleport+command, like said by the school's description but I admit that it could be clearer.

From Spell Description:

Effect

Some spells create or summon things rather than affecting things that are already present.

I can find no Sage Advice regarding the matter, but the rules about unseen attackers starts with this:

Combatants often try to escape their foes' notice by hiding, casting the invisibility spell ...(PHB 195)

This seems to suggest what I believe every table uses: If you are invisible, you attack someone who cannot see you with advantage, even if doing so breaks the invisibility.

Regarding nocking an arrow or swinging back for a punch: this would be a Ready action and not Attack or Cast a Spell, and thus would not end the spell invisibility.

If you cast a spell with a longer casting time

you must spend your action each turn casting the spell (PHB 202)

thus you reveal yourself on the first turn as you have taken a Cast a Spell action.