To me it´s crystal clear that everything must have some meaning,
or else I fear nothing would retain any value at all.
For the Uni-verse is one, since its very beginning,
and objects are just mental images we use to recall
certain experiences separated from the whole.
What is good in one "object" must be in all beings,
and hence it´s not items we need to behold,
but relationships among those items, and patterns, and the good concord
that gives our things their purporse and worth.

But, does any thing have value? If yes, what is that thing? And, how to prove it?

Any thing is a useful concept and therefore has value, if only in a utilitarian sense.

What is any thing? Anything.

How to prove its value? Try referring to anything without using the term that signifies it and you will instantly see its value.

If it has value to you then it has value to you. If it doesn't then it doesn't. There is nothing to prove. If you feel a flower has value to you, but someone else says that flower has no value to them, it still has value to you, and you don't have to prove it you just have to feel it.

I don´t know if value can be established rationally. Some questions just do not have an ultimate answer, becouse Reality itself has no answer, it happens for no good reason. However, we can clarify how phenomena relate to values that all human people share. We share a core of values becouse species who are not favourable to life, freedom and learning about the universe do not survive for long. So there are values that are inherent to entities that remain and pass on their seed to new entities. All Philosophy can do is to help people understand how their behaviour and phenomena contribute to the existence of those values or to their extinction. To show the links, with the help of Science. I guess

Something only has value insofar as some individual values it.