Although your first question was already answered in great detail I'll still try to put it up in simple words for you
but first you'll have to understand that your paint is made up of multiple paint coats underneath some clear coats. Overtime these clear coats start erroding or get inflicted with minor scratches and swirls.
okay now moving to your question...
Polish is a sort of a minor scratch and swirl remover by cutting through those clear coats (that means you lose a clear coat every time you put it) and thus sort of reviving the paint (bad and dull clear coat removed from top)...Polish is from the family of compounds and therefore contains abrasives. People confuse wax with polish, where as they are very different.
Simply a Wax is a protectant. It adds a temporary protective layer over your paint and since it contains no abrasives therefore it's frequent application does not errode your paint. Wax can be a natural wax or it can be synthetic such as Paint sealants. Both normally work in similar ways, it just they both give in a different benefit...sealants give a flat mirror like shine, while natural waxes gives depth.
Glaze...Actually I call glaze a layman's polish...I mean like the polishes that we are used to...jootay pay lagae aur joota chamak gaya...Glazes are liquids which actually add a lacquer like look to your paint and fill in all the scratches and swirls temporary and thus gives it that shine by cleaning the paint and masking the abnormalities...however, a glaze is very short lived and that is why a Glaze falls under the surface prep stage and is always followed up by an application of Wax or sealant or both.
This is how it works...you wash the car with a good shampoo...you get rid of all the accumalated dirt...
Next you prepare the surface for wax/paint sealant...now both these products will enhance the shine which is already there on the car...so if your civic already has dull paint, they alone won't do much difference...
So you apply glaze before wax (well there are other pre-cleaners as well such as Clay/ swirl removers etc. but let's not get into those right now)...glaze will give that shine to your paint.
Then you apply a good sealant or a wax to add longevity to your glaze and to further enhance the look...mirror like shine or that deep deep shine...or both...it is upto you.
Normally after the wax another top coat is given with a detailer (a diluted wax) to add more depth/shine to previous coat...a detailer is also a good way to keep your car shining between wax periods.
Polishes are used rarely as they eat up paint and are only done when heavy corrective work is required and once done you have to again return to the maintenance regime I have discussed above.
Moving to your second point...what you achieved is natural...you used a cheap wax and you got cheap results. You need to invest in a good shampoo, a good wax and a good detailer as a start and you need GLAZE if you wanna mask those infinite circles (called SWIRLS)...and if you wanna remove them then get a good Swirl remover...but using a swirl remover is tricky and RISKY for someone new...better to MASK them at this stage...
