Is one allowed to use a shaker to strain an alcoholic drink on Shabbos? I have been told that it is mutar to use a pitcher with an ice guard on Shabbos, but I do not know the reason why this is not considered borer; the drinker clearly does not want the ice, which I would imagine gives the ice the status of psoles. Does anyone know the source for this heter, and whether it applies to using a shaker for cocktail mixing? Thanks!
Borer is the purification of a mixture using methods reserved for storage, as opposed to eating. For example, when you purify a mixture through removing the unwanted, that is a method that is normally used for storage, not eating.
When you remove the wanted substance from the unwanted with a "purifying instrument", like your pitcher, you have purified using an eating method with one exception: "Purifying instruments" are used for storage, not eating. But in halacha, you are deemed to have used that instrument only if it was practically functional.
The Rema ( O.C. 319:10)paskens that one may purify water from impurities using a strainer since most would drink the water with the impurities (with a possible exception to an istanis acc. to Biur Halacha). Although I would assume manual removal of the impurities from the water would be borer, the instrument cannot be said to be functioning in a halachic sense since the water is already "pure". (It's a fine split, but makes sense.)
Similarly, a posek told me that I may use a salad spinner o Shabbos for a different reason in addition to the Rema. As a senif lehakel, R' Moshe held that a purifying instrument is specifically where it is doing a job which cannot be done manually. The salad may be dried by waving it back and forth. The same is true for the ice water.
In summary, this pitcher is not a functioning kli borer as implied by the halacha.
To answer your beverage question, you would have to post more detail.