Well, the words are

....(yet to be found) SALES

and the explanation goes like this:

You find me attached to many things in life, Many of you throw me out after using that thing.

Many things in life are linked with selling and buying.

Many of you throw me out after using that thing.

( To be provided ...perhaps a shopping bag kind of thing)

Replace a single character with one of mine, I become an ancient language baby name for this rhyme.

Replace last 'S' with 'M'- becoming SALEM, a Hebrew baby name, Hebrew being an ancient language

Break me into two continuous words, Investigate in first with intensities of sound.

This depends on the first word (like: DISCOUNT / OFFER / WEEKEND etc.) ..

Inside, I have a power and skill, and a hollow object to will.

To be provided ...

Well, the words are

DISCOUNT-SALES

and the explanation goes like this:

You find me attached to many things in life, Many of you throw me out after using that thing.

Many things in life are linked with selling and buying.

Many of you throw me out after using that thing.

After using things (which are bought in discount sales!) we normally dispose

Replace a single character with one of mine, I become an ancient language baby name for this rhyme.

Replace last 'S' with 'M'- becoming SALEM, a Hebrew baby name, Hebrew being an ancient language

Break me into two continuous words, Investigate in first with intensities of sound.

DISCOUNT meets the required explanation for intensities of sound, perhaps.

Inside, I have a power and skill, and a hollow object to will.

To be provided ...