Why do Croatian and Italian contain the same grammatical endings for nouns and verbs?

Question

Italy is a country in the Southern Europe. Croatia is a country in the South-Eastern Europe (or Central, depending on interpretation). Because of the close geographical proximity, these two could have influenced each other's languages.

Let's look at some sentences in English, Croatian and Italian:

I drink - Ja pijem - Io bevo
You drink - Ti piješ - Tu bevi
Drink! - Pij! - Bevi!
He drinks - On pije - Lui beve
We drink - Mi pijemo - Noi beviamo
You all drink - Vi pijete - Voi bevete

Ja is similar to io. Ti is similar to tu. The ending -i is the same in imperative. Some verbs in 3rd person singular conjugation have the ending -e. Pijemo and beviamo has root+vowel+"mo". Pijete and bevete end with -ete. Vi and voi are similar.

I wonder why this is so. I also wonder why all other Slavic languages have ja similar to Italian io. This is not only limited to Croatian, but all Slavic languages. How did this happen? Are these languages secretly in a mutual etymological branch, for the lack of terminology experience?

EDIT:

I forgot to add something.

Boy - Dečko - Ragazzo
Boys - Dečki - Ragazzi
Girl - Cura - Ragazza
Girls - Cure - Ragazze

The endings of the nouns with gender and number completely match too!

Answer 1

These all derive from the original Proto-Indo-European inflections.

Compare Classical Latin present-tense verb endings:

  sg     pl
1 amō    amāmus
2 amās   amātis
3 amat   amant

And Ancient Greek (Attic, transliterated):

  sg     pl
1 lȳō    lȳomen
2 lȳeis  lȳete
3 lȳei   lȳousin

And Modern German:

  sg     pl
1 liebe  lieben
2 liebst liebet
3 liebt  lieben

The endings all look rather different, but the connections are clear under the surface. Note also the connection to₂ the -mo and -te endings you noticed: they derived along different paths, from the same source.

The original Proto-Indo-European (thematic active present eventive) endings are reconstructed as something like this:

  sg       pl
1 -mi/-oh₂ -mos
2 -si      -te
3 -ti      -nti

The first-person singular pronouns are also cognates, along with Latin and Greek egō, German ich, English I, French je, and so on: from Proto-Indo-European eǵoH.

(Note: standard "model verbs" were chosen here, so more tables for them are easily found online.)

Answer 2

I'd say it's mostly a coincidence, and maybe some areal influence. The -o in Italian masculine nouns comes from Latin -us, whereas -o in Croatian masculine nouns comes from Proto-Slavic short 'a'. The -i in Italian in masculine plural comes from Latin -i, whereas it comes from Proto-Slavic *y (a sound like the German ü) in Croatian. The -a in Croatian and Italian singular feminine nouns could be related, but the Italian -e in plural comes from earlier -ae, whereas there is nothing like that in the history of Croatian. As for the verbs, the Latin ending for 1st person plural was -mus, far less similar to -mo than Italian -iamo. Similarly, the -te in Italian 2nd person plural comes from Latin -tis. Most of the similarity you cite didn't exist 2'000 years ago, so it's mostly coincidence, and possibly some areal influence, but it isn't due to the distant common ancestor.