If anyone has any insight into any of the 2 questions, I'd greatly
appreciate it.

1) We know that the online perceptron algorithm

can be used to learn a
linear threshold function: w1*x1 + w2*x2 + w3*x3 >= 0". What if,
there's a linear threshold function, and we already KNOW that: a) the
weights of this linear threshold function are always positive b) the
sum of the weights of our linear threshold function do not exceed a
constant W.

How can we use the Perceptron algorithm to learn this particular
linear threshold function? (As in, how would we modify the original
perceptron algorithm to learn this particular function)? And what is
the most number of mistakes we can make with this Perceptron
algorithm?

2) When learning using the perceptron algorithm, imagine there's one
example where the wrong label is shown (eg: output should be 1, but it
falsely told the algorithm that the output is 0). How does this change
the maximum number of mistakes we make with the Perceptron?