Lets check each statement individually.
The horizontal line test is as follows; one checks whether any horizontal line intersects the graph of a function twice or more. If it does not, then the function is 1-1 because any value of y corresponds to at most one x-value. TRUE
A sequence of numbers is a function whose domain are the natural numbers; this has to be so since we "count" the values of the function. This is easy to see if we think of how we describe the values of a sequence:
. FALSE.
A relation is in general a set of pairs where one element of the pair comes from the domain and the other from the output-set. For a relation to be a function, we have that each element of the domain must have one and only one value. Also every single domain value needs to have an output value. This is equivalent to the description, so TRUE.
If a vertical line crosses the graph at 2 points, this means that an input has 2 outputs. As described above, this goes against being a function and is the only requirement for a relation to be a function. Thus, TRUE.