The balck cylinder with a stripe round one of the ends is a diode.
The yellowish square things could be either capacitors of polyfuses but the look like poly fuses to me. You can test this using a multimeter, if they're capacitors they'll read open circuit, if they're polyfuses they'll read short circuit, Polyfuses provide overcurrent protection, they are an example of a positive temperature coefficient resistor, the hotter they get the higher their resistance gets until they barely pass any current. When your circuit is operating normally the low current running isn't enough to heat the polyfuses enough for their resistance to be significant, if there's a short circut a huge current flows the heating in the polyfuse causes it to get hot causing its resistance to rise which causes more heating until very little current flows. If you want more information look it up on Wikipedia.
If you're really confident that this thing won't blow up if it's short circuited then tell your boss that he can trust you and if it doesn't feel that way then shoudn't have given you the task in the first place.
If you're not confident, then explain to your boss that you don't yet have enough experiance to work on this and he should get someone else to look at it even if it means hiring a contractor from another company.
Are you going to college at the moment? Perhaps one of your lecturers might be able to help you.