Adding apricots or Jam to the top?

Ah, baking fruit in the cake batter is indeed different than just laying it on top.

That said, it is possible (e.g., clafoutis) and might actually work with this batter.

If you use an Internet search engine and input "almond torte with apricots" you'll find a number of cakes that successfully accomplish this. Almond and apricot are a natural combination (both are from genus Prunus). You should consider trying this with David Lebovitz's almond cake (the inspiration for this pistachio cake) or the very, very similar Chez Panisse original by Lindsey Shere (labeled almond torte, page 206).

As is typical with cakes where you want pieces of fruits or nuts, you'll have to cut them into small pieces so they are suspended in the batter. If the pieces are too big they will sink to the bottom.

One alternative is to put larger apricot halves on the bottom of the cake pan with the intention of making this an upside-down cake.

There's always the issue of excess moisture from fresh fruit affecting the cake crumb; this is why many cakes use dried fruits instead. Fresh apricots have less moisture than say fresh peaches, nectarines, or plums (three other members of genus Prunus) so this would be less of an issue.

As for the apricot jam swirl, it might be possible to float this on the batter. You could try a small amount and if it immediately starts sinking, just give the batter a quick stir to blend it in. No harm should be done.

Another possibility would be to squirt the jam on top once the cake top sets up a little after a short while in the oven.

Anyhow, now that you have made this cake once per the recipe's instructions, you can consider these alternatives the next time you tackle this.

Generally speaking I think the sensible approach is to follow the directions the first time around before experimenting heavily.