As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.
In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:
A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.
The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.
There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.
On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.
Your use of commas is fine in the five numbered examples you presented, and your career counselor offered you confusing advice about punctuation (even though she may be outstanding at career counseling in general).
In terms of substance, excellent computer skills involve a lot more than typing speed, which is a relatively small part of computer literacy. Far more important is your familiarity with Microsoft Office programs, including Word and Excel, and especially any proprietary or specialized software specific to the industry in which you seek employment.
Speaking strictly for myself, as an employer I am put off by an applicant who thinks it is important to mention his or her typing speed in a cover letter. There are exceptions, of course. If it has been your life-long dream to become a medical transcriptionist, for instance, then it would be very important to highlight that ability, along with an outstanding medical vocabulary, excellent editing skills, and exceptionally good comprehension of spoken English. Otherwise, it just sounds like you are bragging. Please keep in mind that the person who reviews your application probably types at 40 wpm or less. As a Stanford graduate, you hopefully will not spend eight or more hours a day speed-keyboarding, which is extremely tedious and stressful work.
If you want to keep it in, then I would recommend, "I have excellent computer skills and a typing speed of 80 WPM. I'm fluent in [...] Microsoft Word and Excel, as well as [...] Adobe Photoshop and other imaging software" (or CAD/CAM applications, GIS software, or other specialized programs in math, physics, design, layout or whatever else may be required for the job). Under no circumstances should you write, "and therefore I deserve..." anything! An entire generation of students raised with the fantasy that everyone should have high self-esteem (rather than "accurate self-knowledge") has created a false sense of entitlement that clashes with the reality of working in the real world.
The key is always to write for your reader, not for yourself. Put yourself in the employer's position, and ask yourself what you would want a highly qualified applicant to say about herself in her cover letter. Try to avoid cliches and be honest and direct about your experience, education and accomplishments. You'll find that it results in far more positive responses from your prospective employers.
Good luck, and don't worry about your use of commas. You've got it!
Best Answer
You are starting the sentence with an introduction. An indication of time is only one form of introduction.
The fancy term for them adverbial clauses or phrases.