The instruction at the top of a syllogism question always says to take the statements as true even if they contradict common knowledge, and that is the whole trick. "All cats are dogs" is to be accepted without argument.
Draw Venn diagrams. A conclusion follows only if it holds in EVERY diagram you can draw consistent with the statements - one counterexample is enough to reject it.
Try each one before opening the answer. A solution you have read is not a solution you can produce under time pressure, which is the only kind that counts.
Q1 All roses are flowers. Some flowers fade quickly. Conclusion: some roses fade quickly. Does it follow?
No.
Roses sit inside the flower circle, and some flowers fade quickly - but the fading ones may all be the flowers outside the rose circle. Draw it that way and the statements are satisfied while the conclusion fails. One such diagram is enough to reject it.
Q2 All cats are dogs. All dogs are rats. Conclusion: all cats are rats. Does it follow?
Yes.
Cats inside dogs, dogs inside rats, so cats inside rats in every possible drawing. That the statements are nonsense is irrelevant - the instruction says to accept them, and chains of "all" always carry through.
Q3 Some pens are books. Some books are tables. Conclusion: some pens are tables. Does it follow?
No.
The pens that are books and the books that are tables can be entirely different books. Draw pens overlapping the left of the book circle and tables overlapping the right, with no contact, and both statements hold while the conclusion does not. Two "some" statements never chain.