By Rabbi Dovid Ostroff
What is the halacha with regards to cutting up a salad into very small pieces?
Cutting into fine pieces is an offshoot of ‘grinding’ and is forbidden on Shabbos. It therefore follows that it is prohibited to cut vegetables such as cucumbers and tomatoes into fine pieces on Shabbos. However, the Rashba says  that one may cut finely immediately prior to eating, because it is considered ãøê àëéìä, as Chazal did not require one to eat food in large pieces.
Not all agree to the Rashba and indeed the Bais Yosef says that even when one intends eating right away one should not cut the vegetables finely. The Mishna Berura  sides with the Bais Yosef and agrees that one should not cut the vegetables finely but says that one should not rebuke people that do cut them finely. 
However, it is extremely important to be aware that everyone agrees that if one cuts the vegetables finely an hour or two before the meal, or for example one cuts the onions finely and then goes to shul, one is probably liable to bring a korban chatas on account of both Borer – separating and grating the onion. 
Is one permitted to cut meat into fine pieces thereby enabling elderly people to eat it?
Firstly we should realize that since meat does not grow in the earth it is not subject to the constraints of grinding and therefore one may grind meat on Shabbos.  One is forbidden though, to use a grater or meat grinder for this purpose but one may finely cut up the meat with a knife. The same applies to cheese and to any other similarly related item.
Accordingly it is permitted to finely cut meat for small children or for elderly people even though without cutting the meat they would be unable to eat it. 
Am I permitted to chew meat and feed a baby the chewed piece?
Using teeth to grind food for someone else is also considered grinding. Although it is not a d’oraisso because it is a deviation from the normal manner but nevertheless it is forbidden. However, since meat is not subject to the prohibitions of grinding, one may chew a piece of chicken or meat and feed one’s baby the chewed product. It follows that to chew a vegetable or fruit to feed a baby is forbidden  unless done so prior to eating (and even then we learned there is room to be stringent).
Is one permitted to chop onions with an onion chopper on Shabbos?
Even though several poskim hold that one may cut vegetables finely immediately prior to eating (while others hold that one should always cut vegetables into somewhat larger pieces), everyone agrees though, that one may not use a grater to grate vegetables (or any other item for that matter) it being an òåáãà ãçåì – a weekday activity. An onion chopper is in the same category as a grater and may not be used even prior to eating.
Do the regular grinding restrictions apply to biscuits and cakes?
We find a unique rule with regard to the melacha of èçéðä – grinding, which states that àéï èçéðä àçø èçéðä, the literal meaning of which is that once something has been ground in the past it may be grinded again. The problem with this ‘simple’ understanding is that it is an issur d’oraisso (a biblical offence) to grind caked mud  and since mud is comprised of dirt and sand grains, seemingly, according to this rule there should not be a problem to grind mud or mortar.
We find a beautiful explanantion in the Chazon Ish as how to explain this concept of àéï èçéðä àçø èçéðä, which will also clarify our difficulty.
The Chazon Ish  explains that this concept means that one may break up an artificial blend or mixture and the item will not be bound by the constraints of èåçï. Accordingly one may grind or break bread, biscuits, wafers etc. based on the rule of àéï èçéðä àçø èçéðä. Since all these items are artificially blended they are not subject to the issur of grinding. (One may nevertheless not use a grinder or grater it being an òåáãà ãçåì). Thus it is explained why one may not grind mud as mud is not an artificial blend or mixture. 
Where else does this rule apply?
The Rama says  that one may not grind salt but one may grind salt that has caked as a result of cooking or baking. In other words, fine salt grains that merged during cooking may be cut with a knife into small pieces and the Mishna Berura says  that one may cut it finely because àéï èçéðä àçø èçéðä. He adds that the same applies to sugar. Therefore caked salt and sugar may be cut finely with a knife because one is merely returning it to its original state.
Are there any problems removing dried food from a shirt or jacket on Shabbos?
Removing a stain from clothing on Shabbos involves an issur d’oraisso of laundering. We discussed the many details of this melacha in the Shabbos sheet vol. I 16. The pertinent issue is that if mud or dirt splashed onto one’s trousers or jacket, besides having to be aware of the pitfalls of laundering on Shabbos one must avoid grinding the mud or dirt because of èåçï. Food splashes would normally not be subject to the problems of grinding, they would be subject to the regulations of Laundering.
 Rama simon 321:12.
 M”B simon 321:44
 This does not necessarily mean that one should not teach the members of one’s household the correct method of finely cutting vegetables on Shabbos. On the contrary, each person is responsible for the correct conduct of one’s family. It is with regards to others who would normally be offended etc that one need not teach them such a halacha.
 M”B simon 321:44.
 Simon 321:9.
 M”B simon 321:32.
 M”B simon 321:36.
 M”B simon 321:45. See the SS”K 6 footnote 26.
 Chazon Ish Simon 57.
 Obviously one would be prohibited to grind a piece of caked mud that was artificially blended. The reason is probably because the wet mud eventually hardens and binds on its own, åö”ò.
 Simon 321:8.
 Simon 321:30.