Some notes related to acrylic.
There are 2 types of acrylic, one is extruded, the other is cast. The extruded acrylic has a lower melting point, the cast one is easier to machine and is a bit more harder.
Glueing acrylic could be done by something called cement. The brand that seems to be popular in US is Weld-on. There are thinner and thicker cements depending on the usage. I have seen people recommending Weld-on 4 as a starter.
weld-on products are produced by IPS, SciGrip Also there is Evonik Acrifix, mentioned by this thread
In Europe Evonik products seem to be accessible Here is a link to their products
If you don't need the whole 1kg bottle some companies seem to sell smaller amounts as well.
Nice doc on how to machine acrylic sheets