How to make tempura turn out light

As you suggest, there are a number of factors, but the best rule of thumb I've found for pan-frying is to use just enough oil to cover the bottom of the pan by swirling it around. In general, you don't want puddles (you'll get splashed with hot oil), but if the pan isn't covered then your food might not get cooked evenly.

These days I mostly just eyeball it, and err on the generous side. Using slightly too much isn't likely to hurt your dish - unused oil just won't get absorbed - but using too little will result in under-cooked or inconsistently-cooked food and probably a lot of gunk stuck to the bottom of your pan. So if you're not sure, just add a little more than you think you absolutely need.

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.