I wonder why English, Italian, German, Spanish, French and Latin share common alphabet and other words.
Also what is the relation among them.
The western European languages share the Latin alphabet (with minor deviations) because of the cultural dominance of the Roman empire and later the Catholic Church.
Shared words (that a layman recognises as the same) are typically rather recent coinings, often borrowed from the culturally prestigious languages Latin and Classical Greek. Those shared words are found in the domains of science and technology as well as in religion or politics.
The common Indo-European ancestry is blurred by sound shifts and semantical shifts and expert knowledge is needed to discover it. To a layman, the words "tooth" (Englisch) "Zahn" (German) and "dens" (Latin) do not look shared anymore.
When it comes to words, they belong to the same language family called Indo-European (https://en.wikipedia.org/wiki/Indo-European_languages). That means that they had a hypothetical common ancestor thousands of years before called Proto-Indo-European. Spanish and French are in turn Romance languages, which means that Latin is basically their ancestor. English has borrowed a great amount of Latin words (Greek too), but not all words resembling Latin are necessarily Latin, as they might be inherited from Proto-Indo-European. Those aforementioned languages, share also common roots with languages from Eastern and northern Europe, although in some cases you need to have a trained eye to see it. Armenian, Persian and Sanskrit are also Indo-European languages that are/were spoken outside the European continent.
When it comes to the alphabet, Latin derived from Greek that was a phonetic alphabet containing both vowels and consonants. Latin and Greek together spread in all Europe or influenced the creation of other alphabets such as Runic and Cyrillic. Educated Europeans had to know how to read Latin and Greek, hence European grammarians used Latin to write down their own tongue.
Because nations and national languages grew out of a standardization/demarcation of regional spoken dialects which did not have closed borders, and were alike to neighbors (a communication media). Mercantile and military traffic, large migrations, conquerors, the churches all had their influence.
And out of such an amalgam a national language is standardized by institutions (initially literary), and by shaving speech and grammatical constructs to the same style.
Going back still further, humanity took its origin in Africa and then split up. So even American Indian languages may contain a couple of recognizable words.
However development may drift apart, as migration under duress of small groups, that may loose common language.
(In understandable language.)