Congratulations on your new arrival . It can be quite confusing when you first bring them home as there are a lot of conflicting ideas about keeping reptiles.
This site is really good for information and is where I got a lot of help when I got my little Rankins.
1) What you are describing is probably stress of new surroundings. Give him/her time and you should see some activity soon.
They are quite curious creatures and love watching what's going on. My beardies have a good view of the tv and spend a lot of time at the front of their tanks watching it. Make sure you give him water to stop him getting dehydrated. If you can drip some water on his nose and he should lick it off. I use a small syringe I got from the vet but you can use a finger.
2) Slate can get quite hot under a basking lamp and can cause burns to the lizard's belly. They sense temperature with their back and head so often don't realise how hot their belly is getting. I use rocks made from plastic resin and wooden logs which tend not to get too hot.
3) If you are in the UK there are 2 good online sites which I use for all my reptile supplies. http://www.livefoodsbypost.co.uk
. which is brilliant for live food and very quick. The other is http://www.bluelizardreptiles.co.uk
. They are brilliant for tank decorations and also very quick. I have had brilliant service from both sites for the last 3 years. Everything is very carefully packaged and very good quality.
I hope I've been of help. Any worries, post on here and somebody will usually be able to help.
Terri x x x