according my research , most dairy free probiotics today are made by culturing bacteria on a dairy medium ,then using a tech to extract out all milk derivative ,and replace it with chicory e.t.c.which the final product is labeled dairy free and is friendly bacteria in a powder base ;placed in vegi caps ; can I consider this kosher ? or afsher lasochtoi oosir ,and chticha nasse naviela ,?

As much as I would have liked to give you a complete answer and for that purpose I spent some time researching with colleagues in the kashrut field, the final answer to your question can only come from a reliable kashrut agency for a specific product since the food process can change from product to product and from company to company. The kashrut angencies are in touch when in need with food chemists and engineers. I will just raise some of the issues that have to be dealt with as you yourself pointed them out. There is the issue of the source of the bacteria that comes with the milk being from a non-kosher animal. There is then the issue of "ma'amid and its status in regard to production of further probiotic foods. There is the issue of " chaticha naseit naviela" and zeh Vezeh gorem" and then how many times removed from the original raw material does it influence the newer products. There is the issue of "chalav Akum". Also, one must examine if other materials of non- kosher origin flavors, aromas etc. were added to the product. The production line also must be examined. Does the kosher product use the same piping as the non-kosher products and at what temperature? As much as the questions are raised there are sometimes also Halachic solutions. Halachic stringencies may also vary from one kashrut angency to another. In short, you need kosher certification when you want to eat such a product.