Straining pulp from orange juice with a strainer is allowed as it seen as one item. However, for someone who is too sensitive to drink orange juice with pulp, straining the juice would be prohibited as they perceive the pulp to be waste.
There is no prohibition against straining two waste items. For example, pouring a mixture of solids and liquids into one’s sink where the mixture would be strained by the drain ones is permitted.
If water is so impure that most people would not drink it, it is forbidden to strain. However, straining in the process of drinking is permitted. Thus, one can place a cloth over the cup or use a special cup to drink the impure water.
Using a strainer to remove impurities that the vast majority of people do not care about it is permitted. For this reason, using a special filter attached to a faucet is permitted. However, for an individual who would not drink the water if it is not strained, using such a filter would be forbidden.
One may not sift on Shabbos. Sifting is defined as perfecting a mixture using a utensil made for this purpose. (Shabbos Home, page 308)
Biblically, the prohibition is only applicable to items that grow from the ground but the rabbis included all items in the prohibition.
Lastly, it is forbidden to touch fruit that fell from a tree on Shabbos. This is true even if one is unsure as to when they fell.
A further decree around the prohibition of reaping is riding an animal. Since it was common that while riding one would break off a branch in order to use a switch for the animal, the rabbis therefore forbade riding all animals on Shabbos.
Lifting or moving a perforated flower pot that is sitting on soil is forbidden on Shabbos. A non-perforated pot may be moved.