Is a flan a pastry

This is because you are using a microwave. In theory, if you could turn off the microwaves in the microwave oven, you could use the convection function to bake things. In practice, we have had several questions which indicate that this is not how convection microwaves work. They keep nuking your dough, making it inedible. In your case, they are cooking all the moisture locally, resulting in mini-steam-explosions which create blisters, and a dried out, hard and crispy dough.

I am sorry, but there is no way you can bake with a microwave, not short pastry, and not other things. One exception might be quickly eaten "microwave cupcakes" which don't have much flour to start with and are baked for a very short time. I have seen people claim that they work, but never actually tried them.

For baking, you need a non-microwaving oven. The cheapest solution is a toaster oven with a 30x30 cm inner size, they are somewhat trickier to use than a big oven, but good enough for a small budget.

No, this is not puff pastry at all. It is a rich yeast dough, similar to the dough for an unsweetened brioche. The dough has a low hydration (around 50% or maybe 55%), so it can be rolled out into a sheet, similar to a pizza base, without being sticky. In Europe, these are made with AP flour, not bread flour, they are supposed to be soft and not chewy. If you are looking for a recipe, search for brioche recipes with a low amount of sugar which are intended for kneading by hand instead of a mixer.

From the rolled dough, you have to cut a stripe, maybe 1 cm wide. You also need molds for baking. They look like a long cone, maybe 8-10 cm in height and 2-3 cm in base diameter. (You can roll your own from tin halfcircles, if you have the tools to cut a tin sheet into halfcircles). You wind the strip of dough around the cone and bake it with the cone still inside. Afterwards, you have to remove the cone with care, and so you have the hole where you can put the sausage.

I haven't made or seen the variation with eyes. Obviously, you have to add the pips before baking. I am not sure how the white/dark blob is achieved. It looks like something was piped on before baking, maybe normal and colored eggwhite "snow".

The shiny effect of the crust of this picture seems to be due to baking with steam in a commercial oven. You can't replicate it at home, if you want them to be shiny, you may consider using a glaze or wash.