If you're making a hole anything over 1/8" or so, doing it with a hand drill is asking to chip around the edge of the hole. You'll need to get on a drill press, or get one of those jigs to keep your hand drill perpendicular (and steady) to the material.
When cutting, with a jig-saw, you'll want the good surface down
Cutting with a table saw, good surface up...
Glueing - If you can find some of this stuff, you might as well be welding the acrylic pieces together. Brand name is "Weld-On" and product is "#16 cement" If you apply it to two smooth surfaces, it's pretty dam strong, if you apply it to two roughed up surfaces, you'll break the parts before you break the joint. I have no idea where you can get it where you are, but Home Depot's not gonna carry it. I picked it up at a commercial plastics supplier in Langley BC called Laird Plastics (spelling?)
As for cutting, if you want it to be really pro, find a local sign shop and get them to cut it out using a CNC router. Will probably cost you $100 cdn or so, but they'll have the material on hand, and you won't have to do any finish work. Curves all perfectly smooth etc.