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Is there any relationship between -ir verbs and the verb ir itself? I mean do -ir verbs imply going? I can think of salir, venir, vivir (as in life is a path), partir and so. Do they root back to ir?
PS. If so what are the roots of -ar and -er verbs?
No, there is no relation whatsoever between ir and the other verbs that end in -ir in the infinitive.
You should think of Spanish verbs as sets of forms (conjugated forms, with person, number, tense and mood; and the non-conjugated forms like the infinitive, the gerund and the passive participle). The infinitive is just one form, the one traditionally used to refer to the verb and to cite it in dictionaries and the like. The infinitives can be grouped in three classes based on their endings, but that's all. The verbs within a class, when regular, are conjugated in the same way, but they are not related in any other way.
As explained elsewhere, Spanish three verb classes come from Latin. Specifically, the three classes of the dialect of Vulgar Latin that gave rise to Spanish come from the four verbal classes of Classical Latin. The endings -ēre and -ĕre (with long and short e respectively) were merged into one. There was a lot of moving of verbs from the -er class to the -ir class and viceversa, which didn't really affect the conjugation much.
The only thing particular to the -ir verbs is a strong tendency to have high vowels (i, u) in the root when historically they had mid vowels (e, o). That's why cumplir, cubrir, emitir, escribir, recibir have u and i in their next-to-last syllables, even if they are related to completar, cobertura, meter and the old Spanish escrebir and recebir, respectively.
Si y no...
No todos los infinitivos de los verbos terminan en "ir", también están las terminaciones "ar" y "er" ("comprar", "beber").
Pero su etimología proviene de "Ir" que significa "marchar" o "andar", o sea cuando el verbo se encuentra marchando se conjugará con el "ir" dando su infinitivo.
De su misma manera al conjugarse con el resto de los tiempos presenta la misma transformación:
Ejemplo:
Futuro de ir: irás
Vivir : vivirás
