Products available in stores there?

I am also interested to know if housekeeping help and/or part time maids are available in Rakkah and how much do they cost (hourly, weekly and/or monthly basis).

I have only seen Aveeno products once, and that was at a grocery store in Riyadh. You may or may not find Aveeno or the other brands here, but hopefully you can either bring what you need with you or find something acceptable here.

Regarding baby and toddler furniture: Yes, you can find everything you need here. Here are the stores I would recommend you take a look at:
Mothercare (UK based chain)
Toys R Us/Babies R Us
Centerpoint/Baby Shop
Mamas and Papas
IKEA
Pottery Barn Kids

We bought our nursery set from Mothercare. It's solid Oak. I'm now using it for my 3rd baby, and it's still in perfect condition.

We bought our toddler bed from IKEA.

We bought our 'big girl' beds from Pottery Barn.

Even if a product has the same name as what you are used to at home, don't be surprised if the contents are not the same here. We've found that to be true of many household and personal care items. I encoue you to bring at least a year's worth of anything special you'll need for baby, just in case you don't find the brand you're looking for here--or if the contents differ from what you're used to. And if you DO find products here that you like, you'll probably want to stock up, since products come and go, especially if they're not a mainstream item.

We brought an adult bike on the plane as checked luggage. It is considered sports equipment and is not subject to oversized charges, but is subject to excess baggage charges depending on the number of bags you check. The bike store gave us the box it originally came in.

There are bicycle stores here. Limited selection, but not bad for kids bicycles.

Do call the airline you will be on and check that bicycles will be considered sports equipment.