Racconto
Ciao, io mi chiamo Vittoria.
It's not wrong, you can omit "io".
E <s style="background-color: rgb(250, 204, 204);">in mia</s> giardino <s style="background-color: rgb(250, 204, 204);">che</s> un bruco.
"Giardino" is a male noun so you have to use mio instead of "mia". Thus, before "mio" nel is necessary, instead of "in". "Che" means "that" like in "The job that you're doing", so in this case you want to say "there is", which is c'è. It is the abbreviation of "ci è", but it doesn't sound good, so "ci è" is wrong and we say "c'è", like in "chest".
Il bruco si chiama Vladimir. Lo conosco da otto giorni.
Perfect.
Gli piace <s style="background-color: rgb(250, 204, 204);">constuisce </s>un castello di sabbia.
Costruire is correct, which is "to build", while "constuisce" doesn't even exist. I think you meant "costruisce" and the idea is good, but in this case it's wrong. Costruisce is used after "he" or "she", like "Lui costruisce" while here the verb is what he likes, not what he's doing, thus the infinite form is required.
<s style="background-color: rgb(250, 204, 204);">A</s> nel fine settimana spesso fare una passeggiata, anche io.
This requires further explanations. Firstly, "A" is just wrong because it is used to refer to a person like in "A lui, A lei", or a place like in "A Tokyo", "A Mosca" and "Nel" has the same role but with other things. So, those two can't stay together. "Spesso fare" should be changed into fa spesso, unlike before here the verb is not the object, but the action, so the infinite form is wrong and you have to conjugate it. Or, you could use commas to say "Nel fine settimana, spesso, fa una passeggiata". But this is a bit more advanced and you can ignore it.
Lastly, "io" is not wrong, the problem is related to the punctuation. " ; " here is better, because all the part before ", anche io" can be a right sentence alone, so you're just saying something more to it. Instead, if you wish not to use this, which is hated by italians, you can just remove the comma and put an e (and).
E lui è verde.
The sentence is perfect, but in the photos I see him as blue, not green. So if you really meant "green" it's correct. Otherwise, to be extremely precise, blu is correct. I'm fussy, I know.
Ecco <s style="background-color: rgb(250, 204, 204);">tale</s> Vladimir.
"Tale" is not required, only "Ecco Vladimir".