You are not quite right with the second event (event B) in that the second event B is defined in terms of A not happening.
The first event is defined by P(A) = 0.01 but the second event depends on A not happening: in other words B depends on A not taking place (so A^c to represent the complementary event to A) and you are given that P(Delayed Ignition|No Immediate Ignition) = P(B|A^c) = P(B and A^c)/P(A^c) = P(B and A^c)/(1-0.01) = P(B and A^c)/0.99 = 0.01.
So this means that P(B and A^c) = 0.99*0.01 = 0.0099.
The rest of the information can be found using this information, but remember it's important to interpret what the questions ask: whenever one thing depends on another happening, it's always going to be a conditional probability.
You can use this to calculate P(A OR B) but the answer will be a lot different with this new information.