Before staining do you test the moisture content of the wood? Do you recommend any products to test moisture content.
We typically do not bother testing. Most stains can be applied 48 hours after prep or rain without issues but this does, of course, vary based on weather, wood age, and stain brand. If you want to buy a moisture meter to test, it will not matter the brand of meter. Typically 15% or less is a good number for applying the stain.
BTW, some stain brands can be applied to damp wood: https://www.deckstainhelp.com/restore-a-deck-wood-stain-review/