(See question above). Can they all be placed inside a new glass water pitcher that also needs Tevila?

Although one does not drink directly from the pitcher but from the cup or glass one pours the water into, Poskim mention it requires Tevila with a brocho. (Tevilas Kelim 11: 100, p. 217.). However, Horav Shlomo Miller’s Shlit’a opinion is that one should avoid reciting a blessing On question 481 regarding one giving a glass jar as a gift with food inside if it should be immersed first, we wrote: “Horav Shlomo Miller’s Shlit”a opinion is that if the glass jar is used only for the storage of food and not for eating directly from it, it is denominated a k’li oitzer or a storage vessel and does not require tevilah. This is not only true for the giver, who is not using the vessel, but also for the receiver, especially when it is only glass and not a metal vessel. (See also Chelkas Yaakov Y.D. 2: 57, Igrois Moshe Y.D. 2: 40, Tevilas Kelim 4:14).” However, pitchers as they are constantly used on the table require Tevila. (See also q. 2510). One can use the pitcher to contain the shakers. If the pitcher is used to hold the salt and pepper shakers, the opening of the pitcher should be at least 5 cm.