hmm .. i Quick read you questions and ill try to answer as much as i can of em 
1)Which compounds have Mosques close by?
most of the compounds have close mosques to it .. mosques are spread all over riyadh. 
2)Are pampers nappies and SMA formula available?
you can get those either from supermarkets which is also spread in all riyadh or you can get em from pharmacies and there is alot of em here also
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3)Are there any nursery shops I am able to look at online as hubby will have to equip a nursery before I get there.
there lots of baby shops in riyadh dont worry about it.
4)My eldest daughter is currently in cubs in England and my son in Beavers. I noticed on the British School website boys and girls seem to be split between rainbows and brownies and beavers and cubs.
have no information about that sorry, but if you already looked into school for them try to contact it.
5)Is there provision for musical instrument lessons in school as in England?
not sure if they arrange that in schools, but there is always an easy way to find a private classes.
6)This one got to me having just celebrated Christmas and having Children! Really no Christmas trees able to be bought anywhere? Have heard they let in decorations but not trees.
well since i work in a compound i saw few of Christmas trees around so i guess there is places to find them, but where exactly? i dont know :$
7)Bringing things over, how expensive is it to have things container shipped?
have no info about that sorry.
8)I want to bring over personal nik-naks like ornaments, silk flowers, pictures etc etc, is this allowed? I read no statues not sure whether this meant ornaments? Have lots of photo albums I wouldn't want to leave behind. Does anyone have an extensive list of exactly what can and can't be brought over? I wouldn't want anything important being confiscated at customs.
as far as i know most of the things you mentioned no problem for it, but im not sure about statues or anything similar to it.
9)Sky TV. Is it available? If not are there any English channels, kids channels, what is there to watch?
yes its available and there is lots of channels and kids channels to watch.
10)Is internet available? Are you able to download and stream television on the computers?
yes internet is available but dont compare it to the western one :p
11) Have heard houses don't have many electrical sockets is this true? Any electric goods to be brought over do we just use a converter plug or do we need to buy new?
you always can use extensions ..
12)Does anyone know what luggage allowance is available for children coming over by plane? Also heard soft toys are confiscated at customs, going to be a nightmare getting them and clothes into suitcases!
have no information about that sorry.
13)Medication- I am on some meds but cannot find an actual list of banned medication, I only know codeine is one of them.
as Louise said most of meds can be found in here.
14)We have a dog to bring over, have looked into it she won't make a very good guard dog however as she is blind in one eye and is on various medications. Has she to have a complete bill of health to come over?
not sure, but as i heard from friends its not easy to bring a dog over .. but still you can keep asking maybe people knows.
15)Do the shops on the compounds sell english branded foods like Heinz and HP and other English bits and pieces?! Strawberry jam lol!
not sure if you can find every brand you want but i guess there is other choices in markets here. 