Hi, so let me start out by saying that many different people choose to write things slightly different in physics, so I can only speak of the physics I have done myself and have seen floating around during research.
If we want to denote a variable (such as F) to be a vector, we will use the F^ form (which is commonly called F-hat, because the ^ looks like a little hat on the F).
To denote the "intensity" (technically, the right word is "magnitude") of the vector, we typically write two vertical bar on either side of the vector, like so:
||F^||
So, if your teacher is using just F to denote the magnitude, that's just their personal style and you may want to double check with them, as this is NOT (at least from my personal experience) a standard way of denoting magnitude.
As to the second part of your question, if we have two vectors in opposite directions, to do a vector sum of those two vectors, I'm not sure what you've been taught but here's how we generally solve this in physics.
If you want to add only their "intensity"(magnitudes) together, you would find out the magnitude of F1^ and F2^ and add them together, like so:
||F1^|| + ||F2^||.
To find out what the magnitude of the vectors would be, you'll probably have to use Pythagorean theorem. Just do this:
sqrt((x-component)2 +(y-component)2)
Now, if you want to consider their magnitude AND direction, you'll want to add the two vectors component-wise. This means to just take the x-component of F1^ and add it to the x-component of F2^. Then, do the same for the y-components.