Question 1

What are grammatical cases (יחסות)?

Accepted Answer

In Indo-European and some other languages, the function of a word in the sentence is indicated by changing the ending of the word. 
Proto-Indo-European knows eight different cases for which I will give the most important uses:
 
Nominative: subject, default case
Vocative: for addressing one or more persons
Accusative: direct object
Dative: indirect object
Genitive: possession
Locative: place
Instrumental: by means of
Ablative: going to/from
 
Most "strongly inflected" IE languages (e.g., Latin, German, Russian) have two or three cases merged: for instance, in Latin the ablative also subsumes the locative (ablativus locativus) and the instrumental case (instrumentalis).
 
Hebrew has a form of accusative (the prefix "et-"), while the smichut acts like a kind-of genitive. Prefixes "le-" and "be-" can act as a kind of dative and ablative.
 
English still retains a genitive, but otherwise has lost all cases except for the default (nominative).

Question 2

What do you mean, English is a "weakly inflected" language?"

Accepted Answer

In plain English, this means that English gives very few clues about the function of a word in a sentence, aside from word order --- there are no grammatical cases left other than the genitive, verb conjugation is mostly achieved with auxiliary verbs, and the like.
 
As a result, English is much less tolerant of long, convoluted sentences than "strongly inflected" languages like German, Polish, Russian, ... and word order becomes particularly important.

Question 3

This FAQ is under construction

Accepted Answer

Many more answers will be added here.

Question 4

What are countable and uncountable nouns?

Accepted Answer

English nouns come in two kinds that behave differently where it comes to articles and plurals. In plain scientific English:
1. The first kind (count nouns, countable nouns) consists of things that you can "count off", that come in discrete quantities. Think of the concept of a "finite set" or a "countably infinite set" in mathematics. Examples: people, cows, sheets of paper, carbon atoms in a molecule,... 
2. The second kind (mass nouns, uncountable nouns) are either in continuous quantities (water, milk), are abstract concepts (justice, freedom, precision,...),... or are otherwise without number.
 
Count and mass nouns behave differently where it comes to plurals, indefinite articles, and quantifiers. Some other languages have similar distinctions (e.g.  מספר אנשים אבל כמות כסף, but that in English is particularly strict.
 
To make things more complicated, the same word may have both count and mass noun meanings. E.g., "Freedom is never free", vs. "The four freedoms of FDR". 
 
English also has:
3. Collective nouns, which are names for collections or groups of objects, animals, people. A flock of sheep, a gaggle of geese, a soccer team, a rock band,...

Question 5

What is the "aspect" of an English verb?  "

Accepted Answer

Quite simply, it is the distinction whether the action indicated by the verb is:
* currently ongoing/in progress ("currently", from the narration's point of view): continuous/progressive tenses. "I am writing this paper; we are taking this spectrum; as I was driving down Highway 1, Deep Purple's 'Highway Star' was playing from the car radio."
* completed: perfect tenses. "We have synthesized exemplamine; as we had earlier tested the methylated drug and found it not to work, we now..."
* in some other state: imperfect/simple tenses. "I play the piano" (meaning, I do so habitually); "I speak Hebrew" (meaning, I am able to do so); "When Churchill died, millions wept" (narrative past)
 
Hebrew has no concept of aspect. All Indo-European languages I am familiar with have the imperfect-perfect distinction, but many do not have the continuous aspect. French and standard German do not, while some Low-German dialects have the same weak verson as Dutch does ("ik ben aan het schrijven", lit. "I am at the writing", idiom. "I am writing"). Italian, however, has a continuous aspect almost as pervasive as English.

Question 6

What are the most common verb tenses in scientific papers?

Accepted Answer

Most common:
Present perfect for experiments, simulations, etc. you completed and are reporting.
Simple present for unchanging facts of nature, laws of nature,...
Also used:
Imperfect past (simple past, narrative past, preterite) to tell the story of how you got to some milestone
Pluperfect (past perfect) if, while otherwise speaking in the present perfect or imperfect, and referring to something completed earlier. "As we had earlier synthesized exemplamine, we then methylated it to form methylexemplamine."
Present continuous: to describe still ongoing work
Simple future (future imperfect): to describe plans for future work