So what do Jehovah Witnesses really believe?
This is not unlike the question: "How long is a piece of string?". It really rather depends -- on the piece of string.
Officially, the Watch Tower Society's teaching is that Jesus serves as Mediator of the New Covenant, and consequently is Mediator only for those in the New Covenant, viz. the 144 000. The "Other Sheep" are said to be under [emphatically, NOT in] the New Covenant; therefore Jesus cannot be their Mediator. However, in my (limited) experience, very few Witnesses actually believe this.
In public prayer I not infrequently stated that the prayer was offered through our Mediator. On occasion (e.g. meals in our home), I actually apologized to guests for having done so. (I professed to be anointed while affiliated with the Watch Tower religion, and so did feel that Jesus was my Mediator.) Most Witnesses seemed entirely unaware of the Society's teaching. What was disturbing is how many also did not seem to care and would accept the Society's reasoning with no further consideration of the matter.