I am new to go and just starting, and I got confused about some of the rules.
In this picture, is this black’s territory or not?
Also, does black have any territory in this picture?
Well, I’m guessing these are life and death problems that you’re looking at. Just looking at the pictures, they should both be black’s territory. However, if they were life and death problems then top one would definitely be dead.
I’m assuming that the second one is dead too, based on your question. But my reading ability isn’t strong enough to say.
Here’s a demo board explaining it more in depth: https://online-go.com/demo/view/250460
Hope that helps. And let me know if you have any questions.
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depends. If black group can make second eye its black territory, otherwise black is dead. Second is more complex and may also end in seki.
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Let me try to generalize it a little for you.
Any group of connected stones needs to be able to create two eyes to survive. Otherwise (usually later in the game) when it gets completely surrounded it will be captured.
Groups with two eyes are unkillable. Because you cannot play two stones at once to void it of the two liberties and obviously you cannot fill one eye first (and aim for the second later) because it is suicide.
I understand the two pictures are confusing, especially without any context. That’s why it is hard to answer, because black seems to have plenty of room elsewhere (he is not surrounded yet) to find room for many new eyes.
Speaking only locally neither of the black groups can create two eyes. The second picture will really end in seki (considering both players try their best) which is a special case when neither group can kill the other and neither gets points for it.
The first picture is important to understand. I wouldn’t worry about the second at all for now.
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Well-intentioned advice: if you’re just starting, play some games and don’t worry about the intricacies of life and death. It will come to you soon enough. 
If you finish a game that you can’t score, get help from your opponent or from a moderator, or post it here.
As for your questions:
In the first picture, it depends on the surroundings.
In the second picture, black has either 7, 9 or (more than) 11 points of territory, depending on the surroundings and possibly on who plays the next move in the area.
Edit: Sorry, I misread. It would be either 9 points or all black or all white.
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