i saw that there is a weather forecast in pokemon creed? what is the use of having it? what role does it play? does it play a role in battles like in other pokemon games where rain increases accuracy of hydro pump and thunder? or it affects growth of berries in our garden? or does it affect travelling?

No, weather just as you can find kind of items in maps using either Itemfinder or Dowsing Machine

we have a weather system just for that? so, it means while it is raining, you have a better chance of finding something as the soil is wet and can be digged easily. where can i get an itemfinder or the downsing machine? and, what kind of items can i get? can we get a pokemon? can an itemfinder find another itemfinder?

Both of them in Dep. store
Items : Stones, Shards, Ruby, Sapphire, Nugget, Comet Shard, Pearl, Pearl String, Relic Copper, Relic Crown, Relic Band, Balm Mushroom.

can you tell a fair estimate of how much each of them is worth? in coins? stones are used to evolve pokemon like vulpix and growlithe and eevee, other than stones, i do't know use of any other item? and, how to use itemfinder? it is very costly, if finding items and selling them is worth it, i will save for an itemfinder.

Check here : [you must login to view links]
You need equip it in [Manage Items] -> [Equip Items]

and then, while we are walking around, we will get it like we see a wild pokemon appeared?

yes, that's right :)