1. Is there determinism?
2. Because we can't measure the electron position, it doesn't mean there's no determinism?
Heisenberg uncertainity principle states, per wiki:

But because we can't measure it, it doesn't mean that the universe itself is indeterministic? Everything should be determined right from the beginning? Even if there's no (or there will be?) technology to measure even the movement of 1 electron?

Simply typing "determinism" in Google returns:
"Determinism is the philosophical idea that every event or state of affairs, including every human decision and action, is the inevitable and necessary consequence of antecedent states of affairs."

In (classical) physics, given the initial position and momentum of an object, one can determine its position and momentum at some later time with 100% certainty using Newton's equation of motion, that's how one usually describe deterministicm in the context of physics. In quantum mechanics, there's no such a thing as determistic measurement upon a system if you don't know what kind of measurement previously performed on this system or, if you know what quantity previously measured, but the quantity you are currently measuring is incomaptible with the previous one. A prime example of incompatible pair of quantities are position and momentum, which gives rise to the renowned Heisenberg uncertainty principle. The only deterministic aspect of quantum mechanics, as far as I know, is the time evolution of a system. Given the initial state of the system as well as the corresponding Hamiltonian, you can predict with 100% certainty what the state will be at some later time.

We can measure the position of a particle, it's just that it's generally not possible to predict with a perfect certainty what number will come out of our measuring device.

Secondly there are interpretations (eg BM) of QM that are deterministic in the sense of classical physics.

That said the formalism of QM is generally considered deterministic because the state obeys Schrödinger's equation which is a deterministic partial differential equation.

Thank you blue_leaf77
Thank you bhobba, for your answers.
I'm considering your answers. But I'd like to ask about this phrase. Perhaps you could elaborate a little.

It's not possible to predict with a perfect certainity what number will come out?
I mean this.
You have a thermometer, and you INTENT to measure the temperature of your hot tea. But of course you cannot predict what is its temperature BEFORE you put your thermometer can you?
And if you CAN predict what the temperature of your hot tea, what is the purpose of measuring it with thermometer? All you have to do is stare at your cup and say, "A ah it's 70^{0}C".
What do you mean by "It's not possible to predict the outcome"?
Thank you very much.

The key thing, and its not something that can be explained at the lay level, is we have interpretations where that randomness is explained by a deterministic theory and others where it's fundamental. That's one reason why the question you are asking doesn't really have a definite answer.

Imagine you have a loaded dice. How its loaded determines the probability of what happens if you throw it. How its loaded corresponds to what's called the quantum state. That varies deterministically and that is the sense everyone agrees QM is deterministic. How the loading determines the outcome of throwing it is the debate on if QM is fundamentally deterministic or not.

1. As mentioned, no one knows the precise answer to this. This is a matter of what interpretation of QM you subscribe to, and there is currently no science to differentiate.
2. There is no specific limit to measuring the position of a quantum particle. As you more accurately measure the position, its momentum becomes undefined. This is not specifically related to the physical act of measurement "disturbing" in the ordinary sense.

What is meant by the random outcome of a measurement in QM is not exactly like that. It's more about the results of repeated measurements over the same system (same state) rather than a single measurement as you make an example of above.

In your thermometer example, so long as you can keep the temperature of the tea at 70^{0}C, repeated temperature measurements will always return a value of 70^{0}C (disregarding any small fluctuations which might as well has its quantum origin). This is not the case with quantum system. Let's take an example of the famous Stern-Gerlach experiment. A beam of silver atoms is sent through a magnetic field pointing in the z direction, this magnetic field has uniform direction but varying strength in order to separate the atoms into up and down spin. Another magnetic field with the same characteristic is put in the line of the up spin atoms, but this time the field is in the x direction so it will deflect the incoming atoms out to the left or to the right. With this arrangement, we can be sure that the state of all atoms that are registered to the second magnetic field is of the up spin state.
The first atom starts its course through the pair of perpendicularly oriented magnetic fields, and suppose this atom turns out to be deflected to the left after the second field. The second atom, which is also going be in the up spin state when entering the second magnetic field, however, does not necessarily be deflected to the left as the first atom was. In fact, if you repeat this procedure over sufficiently many number of atoms, you will find that there are as many number of atoms deflected to the right as those are to the right.