That is the "Maidenhair tree" Ginkgo biloba
The fruit is smelly (like vomit) but the seeds are edible, and used in Chinese and Japanese cuisine. It has attractive yellow leaves in the autumn.
It is a relic species, not closely related to other modern trees.
This is an euphorbia hybrid (naming varies, including E. hypericifolia, E. graminea, or a hybrid with one of those species, or Chamaesyce hypericifolia), the trade name is Diamond Frost.
The German name is Zauberschnee (“magic snow”) and in recent years it has been a quite popular plant for container gardening and window boxes.
Those „eggs” are not eggs, but cabbage aphids at different stages of maturity. They feed exclusively on brassicaceae, so other non-brassica plants nearby remain safe.
In dry summers they can cause severe damage and multiply very quickly. Like all aphids they suck the plants’ sap and when the infestation is severe, cause the leaves to shrivel and prevent ...
Very likely a Dracaena type, maybe marginata , especially if leaf edges were redish color. It looks pretty far gone with the wrinkled bark, they can grow from dead looking wood. Normally very tolerant, my biggest problem is deciding what to cut off when bringing it in from the deck for the winter.
likely heavy watering after it was ripe. At some point in maturity the skin loses most of its flexibility and if the fruit expands with good water supply it can split the skin. I would say eat it or cook it as soon as possible because various molds, etc. can have access at the split skin.
I'm pretty sure that's a moss rose (Portulaca grandiflora). It's grown as an outdoor annual in the US and has single, semi-double, and double flowered forms. Single-flowered forms are not as popular as the other forms. They reseed readily and can become kind of a pest if you don't use mulch in your garden. The flower habit you mention of opening for only a ...
Common name is Apple-of-Peru, botanical name is Nicandra physalodes.
It is a member of the Nightshade family, and as the name suggests already it is native to South America. It is introduced in many parts of the world including Europe.
If you want to propagate it, try to collect seeds.
I'm guessing that your mother cooks with what in the US we call a squash. It looks like it's a green striped cushaw (more info here) , but of course it could easily be a variety specific to your region of Italy. Cushaws are a winter squash and harvested when the rinds are hard. According to SF Gate:
Look at your cushaw and determine if its color has ...
They look like spittlebugs. They produce a bubbly spit-like substance around themselves for protection from heat, predators, etc. Your reply to me question seems to confirm this. Apparently, they can be plant-sucking pests, but I've only seen them on rare occasions in small numbers before (mostly in my childhood on giant garden weeds), and the plants didn't ...
It looks like a crab spider of some kind. There are lots of kinds.
Here are some links with pictures that look like yours:
https://naturegardensnhm.blogspot.com/2012/02/killer-legs-crab-spider-wins-prize-with.html (This one's a white-banded crab spider.)
Supposedly, crab spiders can change colors (so, ...
This is mealy bug and hard to get rid of on palms as they hide in the leaf sheaths surrounding the new growth.
More details are here but soap and water or neem oil applied at least three times at five to six day intervals are where you want to start.
Try persimmon or Texas persimmon ; diospyros. They have fruit that looks like photo and holds until late summer and fall with little predation by insects or birds.
Leaves also look right. The TX variety is listed as shrub up to 40 ft. Bark with deep fissures that tend to make a checkered pattern ( characteristic pattern). Personally the fruit is very ...