As far as I know, the word "steak" can only be pronounced as the "a" in "bake."

I have never heard "littler" used, however it is in my English dictionary. I assume that most English grammarians would say that one should usually (if not always) use "smaller" instead of "littler."

But I could be wrong. I haven't heard everything! :-)

I agree with Dave Ratzinger, er, I mean, Dave Rattigan.

I am not aware of any prescriptive rule which tells us whether to say "Jane" or "you" first. I agree with Steve, in that it sounds a bit more natural to me to have "you" first, perhaps as a way of expressing politeness to the closest addressee. But I don't think there is any rule or advice that would be against saying "Jane" first in the sentence.

I also agree with Steve that "you guys" is very widely used these days, both for males, females, and mixed groups of females and males. It would be perfectly acceptable to use as a substitute for "you and Jane," is both speaker and hearer understand who "you guys" refers to.

Both females and males use "you guys" to refer to all possible combinations of males and females.

Here's what I was taught: Use the "case" of the pronoun that you would if the other person's name is taken out of the sentence. For instance, in your sentence, if you remove Jim, your two pronoun options give you:

1. I discussed the proposal that was sent.
2. Me discussed the proposal that was sent.

Most fluent speakers of English would say that #2 is ungrammatical. Therefore, according to the grammarians, the nominative case "I" is the proper form of the pronoun to use in your sentence when Jim is included.

Having said that, I am hearing more and more people speak sentences using the "me" form of the pronoun, rather than "I," when there is a conjoined phrase as you have in your sentence. So, once again, we are left with the question of how long do we wait and for what percentage of speakers before we language usage change as being "acceptable"?

It depends on what you mean by "correct." If you mean what is right according to grammar rules, then several others have already posted the "correct" answer, which is what I was taught in school, namely,

"My mother bought some sweets for my sister and me."

Here is what I was taught:

1. When a pronoun is the object of a preposition, which we have in the word "for" here, use the objective case which would be "me" for the first person singular pronoun.

2. Put the other person's name before your own to show that you are being polite.

Now, as to what is truly "correct," that is open to debate. I still cringe when I hear English speakers using the nominative case after a preposition, as in

"My mother bought some sweets for my sister and I."

But many, many native, fluent English speakers are talking and writing this way these days. They do it automatically. They are not using the nominative case to make some social statement. It is simply that English language usage for pronouns is changing. If enough English speakers adopt this new usage, eventually there will be few speakers left who still follow the pronoun rules I was taught. Then a shift will take place where those who say what is "correct" and incorrect usage will have to give up and accept the new usage, just as strict grammarians eventually had to give up requiring people to use different pronouns for second person singular and plural, such as "thee" and "ye."

Descriptive linguists, who do not advocate sloppy speech, would say, in this case, that usage determines what is correct or not. Most English teachers disagree with them. If you associate with people who no longer use the objective form of pronouns after a prepositions, you need to be aware that you may be perceived by them to be "uppity" if you use the form taught by prescriptive grammarians. If you don't mind being perceived as "uppity", and, in fact, take pride in using "correct" speech then use the forms taught by English teachers. Just be aware that usage of some language forms does create some social perceptions that we may not intend.

It looks like this is no rule, unless euphony is a factor.

Yes, I've heard "You've gotta be joking me." From a descriptive POV, I don't think we can say it is right or wrong. It's right for the dialect of the person saying it. My grandmother (not a native speaker of English, but she learned to speak English) used to say, "I just joshing you." :-)