If my backyard was flooded with rain, am I permitted to place boards to flatten the surface?

This issue involves the problem of adding substance to a ground or building, which entails the melacha of Boneh. In this case one obviously does not intend for the boards to remain there and they are only a means to enable one to traverse the backyard without getting wet. Therefore there is no problem placing boards (that are not muktze) [1] over puddles etc. in the street (where there is an eiruv), backyard or lawn. [2]

What may be done on Shabbos with regards to icy sidewalks/pathways? May salt or sand be spread over the ice?

This is more complicated than the previous question, because the ice and sand are not removed subsequent to the ice’s melting. As far as pouring salt on ice is concerned we can safely say that since the salt melts and does not remain on the sidewalk or in the yard it is not Boneh. However spreading sand on an icy sidewalk might involve the issur of Boneh; The Sh’miras Shabbos Kehilchasa [3] says that one is permitted to pour sand on an icy sidewalk and Rav Eliyahu Falk [4] says that it is forbidden because the sand remains in place and is a problem of Boneh. [5] Accordingly a halachic authority must be consulted.

My new tin of Nescafe is sealed with a piece of aluminum foil. Am I permitted to rip it open on Shabbos or is it Tearing?

There is a Tosefta in Shabbos 17:9 that says the following: "One is permitted to rip the leather covering a barrel's opening provided that one does not intend making a spout". This means that it is permitted to tear the leather, or any covering for that matter, that covers a barrel in order to retrieve the barrel's contents.

The question is though that we know that tearing paper or leather is forbidden on Shabbos; if done in a constructive manner it involves a Biblical transgression and if done in a destructive manner it involves a rabbinical one.

The Rambam says (10:10) that, one who tears in order to destruct is exempt (from a biblical punishment), but nevertheless is forbidden to do so, so why should it be permitted when fixed to a barrel?

The sefer Sh'visas HaShabbos explains that rags or leather wrapping food or drink become part of the food just as a nutshell is part of the nut, and just as one is permitted to crack open a nut, so too one is permitted to tear the paper or leather encasing food.

The Sh'visas HaShabbos adds that "it becomes like other detached materials where Kore'ah – Tearing is not applicable". Accordingly, it is permitted to tear the aluminum foil sealing the coffee. [6] We will explain this in more detail soon

I was presented on Shabbos with a piece of veal tied in a net and did not know how to proceed. Was I permitted to slice the string?

The Shulchan Aruch [7] says that one is permitted to cut through string tying roast meat or fowl to the spit. The explanation being, as the poskim [8] put it, that string is not a k'li and when not cut to size or for a constructive purpose it is permitted outright.

Since the string encasing the meat is not cut to size, nor - as far as the string is concerned - is it cut for a constructive purpose (it is immaterial that I have an indirect benefit from cutting the string), it is permitted.

Why then does the Rambam, quoted previously, say that one is forbidden to rip or tear something destructively?

The P'ri Megadim [9] answered this question saying that a garment, leather or paper are considered keilim and tearing them is akin to destroying a k'li, which is a rabbinical prohibition. Conversely, a piece of string or rope is not considered a k'li and therefore its tearing for no purpose is not an issur at all.

We can now understand the Sh'visas HaShabbos we mentioned above that said that the leather becomes like a detached item i.e. a non-kli and as such Tearing does not apply.

The Shulchan Aruch HaRav [10] also used the term of cutting a detached item.

Would this imply that I am permitted to tear any cellophane wrapping, whether it be for food, clothing etc?

Correct, because the cellophane wrapper becomes part of the contents and is not looked at as a separate entity, thereby permitting tearing the wrapper to retrieve the contents.

Rav Shlomo Zalman Auerbach Ztz"l [11] learns from this Sh'visas HaShabbos that one may open any packaging that is not reused after its contents have been emptied (the Rav holds that one need not empty the contents upon opening, nor must the packaging be opened in a destroying manner, but that is a separate issue) because of this very reason. The Rav did not restrict this rule to food wrappings, because this reason applies to clothes and toys as well.