Hello!
Well, I am not that much into levers, so no info on no. 2.
1. Not tested in 39c, but until 38c at least, cats and dogs did not fight (at least not in a notable way).
Personally, I would not recommend taking dogs with you, though. And this is not only because I am not only a cat-lover but also a dog-hater :) :) :)
Your pets have a tendency to breed, and breed quite rapidly. There is no way for you to stop them from doing so, except for exploiting some bugs which may or may not be still around.
This would not be a problem if the program did not keep track of all your pets allowing them to make their own decisions and move freely (provided they are not caged). So, if your pet population grows, you may face a decreasing frame rate (=game speed).
This is why you see all the discussions about ways of removing those useless puppies or murdering poor kittens en masse.
Thus, taking unessential animals with you on embark may mean risking troubles with game speed early on (on embark, you can't determine the sex of the animals, but if you have three of a kind, you can assume that they are a breeding combination).
As mentioned above, breeding is hardly controllable, and partially allowing it is very difficult since you need to influence the animals via jobs given to your dwarves (like butcher puppy or cage cat) - and you may have noticed that dwarves will not always do the jobs in the order you like, so there may be a long delay - maybe too long to prevent the next generation.
Take note, however, that leaving away dogs is a design decision for your fortress.
Basically, you currently have the option of centering your defenses either on army or traps. For beginners or people not interested so much in military detail, traps are the better solution as they are easily to build and quite reliable with most enemies. Training and organizing an army takes more skill, especially since some parts of that take quite a bit of managing. Personally, I recommend to picking that challenge only once you feel firm with the basics.
With a trap-centered defense, you do not need many military dwarves (eventually, when you get real sieges, you may wish to get a few archers, but until then, you rarely need regular military).
If you choose the military approach however, you need to train and organize an army quite quickly. Assigning (war) dogs to fight alongside your soldiers is an option to strengthen them and reduce on-job casualties. So, dogs are part of your soldiers' equipment in that case.
About the bridges and levers, one comment though:
Don't underestimate dwarvish lag. Dwarves will finish what they are currently doing before taking on a new regular job like pulling a lever (and only dwarves can pull a lever, you as the player can not do so directly), pulling a lever does not have a very high priority, it seems and dwarves may stop doing a job if they get hungry, sleepy, or thirsty - even if they are but one tile away from that lever.
In the early stages of your fortress, your dwarves will probably be busy doing all sorts of things, so if your defenses rely on someone quickly pulling that lever, things can easily get dangerous.
Later on, when you have a lot of population and a few non-functional nobles, levers become more reliable as you have more people without any other proper jobs (non-functional nobles will only participate in harvesting - if that is enabled, pulling levers, and health care, I think, though I am not sure about the last one, so they are often idle and thus can respond immediately to pull lever demands)
Have fun.
Deathworks