Can potato gnocchi dough be overworked or simply break

You're on the right track! Start adding your flour in the bowl as you did and when you can remove it without it being too tacky then start working it on a cutting board or countertop as you continue adding more flour. Sounds like maybe you pulled it out of the bowl too soon.

As for a specific ratio of flour to potatoes/veg. that's going to depend not only on the items you're using, but also cooking method (for instance I recommend baking potatoes for making gnocchi rather than boiling as they will be drier and need less flour added, thus making for a lighter dumpling).

Once you have enough flour in the mix so that you can knead it and work it, I usually do a "stretch" or "tug" test but holding the dough up in the air and with my hands at each end and then kind of pull and push the dough from the ends (hard to explain in text but imagine the push and pull of two magnets you're trying to push together). If it has a bit of tug and a little elasticity you should be fine. If it doesn't, then either knead it a bit more, adding flour only if it is sticky. If it still doesn't have any tug after kneading more, then you probably don't have enough flour. The gluten in the flour is what's going to help hold it all together so that you don't just end up with disintegrating mashed potato/vegetable blobs in your poaching water. If you're making a big batch it will probably take longer than you expect to get it to the right consistency.

As for types of flour, the more protein a flour contains the more liquid it can absorb. While I have not made gnocchi with bread flour, it would take less bread flour than all-purpose to absorb the moisture in the mix. It will also have a more distinct flavor from the add'l protein. One caveat is that it could end up making them too tough due to the extra gluten.

If the exterior of the gnocchi you had at the restaurant was crispy in the sense that it had a crunch to it, then they probably dropped it in a deep fryer for a minute or so to crisp it up.

I usually saute mine in clarified butter to brown the exterior and form a crust but it's not necessarily "crispy".

Regardless of what you're frying and whether you're shallow or deep-frying it, the problem of absorbing oil and turning out greasy is due to not having your oil hot enough, or adding too much food at once and dropping the temperature too much.

You usually want to fry between 350 and 375 degrees. If you're using a thermostat controlled fryer or electric skillet, then I suggest setting the temperature at 365 degrees so you still have room for up to a 15 degree drop in temperature without detriment to the food.

When food is fried the oil heats up the moisture inside the food product which then turns to steam and forces its way out. As the steam pushes outward it creates the visible bubbles we see. It's the force of the steam pushing outward that keeps the oil from going in to the food. As the temperature drops and thus the pressure from the steam, or the moisture has cooked away and food isn't removed when its done, the food starts to absorb the oil and turn greasy.