Problem is that Q usually represents the K sound (usually in combination with U) in most European languages, and Zamenhof had already drafted K for that purpose -- why have two letters for the same sound? To use it for the Hx sound, as is done in many latinizations of Hebrew and Arabic, would sound too foreign; and the Pinyin Romanization of Chinese, in which it is used for Cx, was not yet in use. Furthermore, there is no equivalent of Q in the Cyrillic alphabet. Zamenhof apparently felt justified in dropping it.
W instead of Ux? Problem is that W has this sound primarily in English and some Romance languages (it is rare in the latter); in the Germanic languages and those Slavic languages that are written with Latin letters, W usually has the sound of V (or, at the ends of words, sometimes F). Since V and F already existed, and since the use of the English W would be very foreign to Zamenhof's original clientele, he felt justified in omitting the letter.
X is an extremely non-standard letter; in some languages (Spanish, Russian) it has the value of the Esperanto Hx, in some (Portuguese, Chinese Pinyin) it has the sound of the russian Sx, in French it is often silent. Furthermore, its use in English and other languages is really for a combination of two sounds, KS (or, sometimes, GZ), and Zamenhof's principles did not allow him to use one letter for two separate sounds. So he dropped X.
We often tend to assume that Y always has the sound of the Esperanto J. This is often the case, even in languages other than English, but not always. In the Germanic and Slavic languages, for instance, this sound is represented by J, as in Esperanto. Furthermore, in the Scandinavian languages Y has the sound of the German umlauted U. Since J (which see) was so familiar to Zamenhof's original clientele, he decided to drop Y.
Zamenhof could not use a digraph such as CH for that sound, since C and H have independent sounds of their own. The soft G (often shown by a J in English) needed to be distinguished from the hard G; in many languages this is determined by the following vowel (soft before E and I, hard before A, O and U), but the letter G in Esperanto was allowed to have only one sound, independent of the letters around it. The rasped sound halfway between K and H (written CH in German and Gaelic, X in Russian and Spanish) needed a letter to represent it. The soft J (written J in French, S in English) needed a separate letter; here Zamenhof was apparently influenced by French usage. Similarly to CH, the letters SH already had independent sounds, and anyway digraphs were banned. Finally, for reasons given above, a letter was needed for the English W sound, but Zamenhof did not want to use W. Hence the six special letters.
Truth to tell, four of those supersigned letters could have been replaced by the four standard letters, by some judicious juggling: Q->Cx, Y->J, J->Jx or Gx, X->Sx, W->Ux. The changes, if they had been made in 1887, would not have been bothersome. Still, that would have left two unrepresented sounds (Gx or Jx, and Hx) for which special letters would have been necessary; and if you can't avoid introducing two special letters, why not go the whole route and introduce six?
Other workarounds are sometimes used, and you should be aware of these. The officially sanctioned method, actually included in the Fundamento de Esperanto, is the use of the digraphs CH, GH, HH, JH, SH; U without a supersign does double duty for U and Ux. Zamenhof himself used this method in telegrams (there are International Code characters for the Esperanto letters, but telegraphers who are familiar with them are few and far between). The method has its proponents, but, due to the fact that C and H are both Esperanto letters and can be inadvertently joined during the process of agglutination, it is better avoided. X has the advantage of not appearing anywhere in Esperanto words.
Other symbols are used as well. You will find ^C, C^, Cy, and others. Cx is preferred; but if you don't like it, feel free to use your own system.
For A, as for every other vowel, the sound should be clearly heard, not muted, even in an unstressed final syllable. This is particularly important for the verb endings, where the present -AS and the future -OS can be easily confused if you follow the American (and Russian) habit of muting unstressed vowels.
Note that this is one single sound, not two; in almost every case, the English spelling TS is a spelling convenience for a single sound for which a single letter is lacking. This is even true in cases where the sound was originally a combination of two separate sounds; if you listen to the word RATS carefully, you'll find that it's not just a combination of T followed by S, but an actual different sound, about halfway between the two.
This is often true even when the sound is formed by a juncture of two words. The standard pronunciation of BEST-SELLER, for instance, is not (using Esperanto letters) BEST-SELR but BES-CELR.
As mentioned above, English-speakers sometimes try to suggest that C is really a combination of two sounds, T and S. French- and German-speakers, in addition, will occasionally make the claim that the 'Cx' sound is a combination of two sounds, T and Sx (English T and SH), since in both languages our CH is often spelled TCH (in French, CH is pronounced like our SH). Actually, once again Cx is about halfway between T and Sx, but is an independent sound in its own right. Fortunately, very few English speakers have as much trouble understanding this as they do understanding the corresponding independence of C.
It is pronounced with the tongue bowed down in the middle, and the tongue tip raised to touch the juncture between the front teeth and the gums. You flap the tongue perhaps twice while forcing air out between the tongue and the teeth. This gives you an R with a slight Scottish burr or Spanish trill. I keep the tongue-tip slightly to the right of center, myself.
There are usually secondary accents on even-numbered vowels (counting from the end of the word). One exception to this is that MAL-words (which you'll meet in lesson two) usually get a slight stress on the MAL-prefix, even when it is in an odd-numbered position.