"...Does this limp-wristing jam cause any permanent damage?..." Not at all. It's operator failure. No big deal. Think in terms of the slide needing some resistance to work properly. Your hand provides that resistance by holding the frame in place.
"...because the brass did not eject correctly..." Yes and no. A jam can be a feeding issue or an extraction/ejection issue. Feeding issues, ammo being stripped from the mag and sent into the chamber, are usually mag related. Extraction/ejection issues, the case being pulled out of the chamber and thrown out of the pistol, are usually ammo or dirt related.
"...how do you go about a first clean?..." Same way you normally clean it. Field strip and use a solvent and patches. Got a cleaning kit? A manual? Go here for a free, downloadable .pdf manual, if you don't.
http://stevespages.com/pdf/glock.pdf
"...Should I do it ASAP?..." You really should clean it after every day at the range. It's not going to dissolve if you leave it for a few days though.
Cops that carry Glocks rarely do any regular maintenance. Worked in a gun shop, long ago, when cops, up here, still carried revolvers and were only allowed to change the grips. A plain clothes cop came in one day, went to unload to try a set of grips. His service revolver was rusted shut. A pair of 'em came in another time. One guy bought a set of grips. The other guy decided to try a set on his revolver. Reached for it only to find he had left it at home. Had the holster but no gun. His partner went ballistic. Most cops are good guys, but they regard their service piece as a piece of kit they're required to lug around. Most of 'em can't shoot worth beans either.
"...Sorry for all these questions..." No need to apologise. Shooters help new shooters regularly. Go join a shooting club. You'll meet some of the greatest people you'll ever know and most will bend over backwards to help you. Including letting you try their firearms. Belonging to a shooting club opens all kinds of other doors too.