Hi
@grannybaker
Yes, you can make a buttercream layer cake with 3 - 4 layers depending on how good the structure of your layers are. If you just filled it with buttercream and decorated the top, then the structure of the layers wouldn't be that much of an issue, but because you're adding weight with the icing fondant you'll need to ensure the cake has a good structure. Otherwise, it will sag.
When I make a birthday cake, I tend to make a full cake and then cut it into layers; I do this because I find a full cake cut into layers doesn't give me ridges in the sides and holds its structure (I tend to use a Madeira cake for birthday's because it has a denser crumb, but you can use victoria sponge, but again I would make two cakes and then cut them into layers. But that's me. You do what works best for you.
I cover my cakes in jam to stick my icing fondant to it because I'm not a lover of buttercream, but it you are using buttercream, you will have to crumb coat it first and then apply another layer before you cover it with fondant.
For easiness, I tend to put buttercream in the centre, then cover in jam and then cover in fondant so you don't have to faff about waiting for a crumb coat, but that's just me. You also have to ensure that you use enough buttercream to stick the icing but not too much that it eats through the icing.
Regarding the buttercream, if it is regular buttercream with butter/icing sugar and a touch of milk, it will be fine sealed in a cake for a few days (even sometimes up to a week) as long as you store it in a cool place where it won't melt.
I'm not quite sure what kind of cake you are thinking of making, but here are a few links to tutorials I have done to see if they help you.

My daughter recently asked me if I would make a cake for one of her close friend's Great Nan's 100th birthday, and I thought it would be the perfect opportunity to make the milestone cake and use one of the sparkly cake toppers at the same time.
After being informed that the cake was for a small gathering, I set about sourcing a cake topper to give the cake some height and a little bit of bling. (If you make it to 100 years old, you want to have something a little extra...
I've put together a step by step guide showing you an easy way of rolling out your icing fondant or marzipan and then applying it to your cake.
- Please note that for sponge cakes, buttercream, jam and frosting form an adhesive that allows your icing/fondant to stick to your cake.
- However, if you have a fruit cake that needs to be covered, use apricot jam as the adhesive and ensure you marzipan and icing/fondant it also. This is because the fruit from the cake can bleed through onto a single layer of icing.
Before we get started, I need to mention that if you are...
In order to ensure you have enough icing rolled out, you can use a handy trick.
Get a piece of ribbon and place it on the end of you cake board (before using buttercream or jam etc.) then place the ribbon across the edge then up the side of the cake over the cake, down the other side of the cake and to the edge of the board as per picture 1.
When stretched out, this will give you a rough idea of how wide the icing/fondant needs to be in order to cover your cake.
Now see illustration 2, if you roll your icing out to the length of the ribbon both lengthways and widthways it will...
I hope I haven't overloaded you with info, but if you need anything else then let me know.
Best wishes
Angie