Pro tip: Use the Dwarf Fortress Wiki! It is pretty much perfect as far as community-created wikis go.
You are right around the point where the first immigration wave is set to start - starting with autumn or summer. If you were producing stone crafts 24/7 for several seasons I even think you'll be getting 15 dwarves or something like that, i. e. a tripling of your previous population. So yes, a bit more patience is advised, they will come.
Trade agreements function in the way that you select certain items you are willing to pay higher price for - up and down keys select items, + and - keys select item groups, left and right keys set the demand level. Basically you think "Hmm, what does my fortress really need" and increase the demand level for that. The caravan will bring these items in higher number the next year. In return, the caravan leader will do the same; he will be willing to pay higher prices for certain items (up to just over 200% price increase actually), but he will only do that if you're willing to tell HIM what you would be willing to pay higher prices for - that's why it's a trade agreement. This whole shebang has nothing do with why you didn't get immigrations yet - as I said, just be a bit more patient; the existence of the dwarven caravan proves that the dwarven civilization still exists, after all. Immigration is a random thing; sometimes I got immigration waves before the first winter.
z axis: Well, you shift in z axis the same way you climb stairs in ADOM, so the trick to this is to just build stairs Every stairwell consists of at least two parts, the down staircase built on the upper level and the up staircase built on the lower level. You can dig the stairs out of the stone, and if you've dug out the down staircase you can dig out the up staircase from above. What do you use this for? Well, the same reasons why houses generally are built with several stories; shorter walking, more efficient design. It becomes more complicated once you try to build structures outside; in the beginning I advise staying indoors and making a nice dwarfy underground/mountain fortress using your miners.
water supply: You want one because bed-ridden dwarves for some reason may only drink water, so they will die of thirst if the other dwarves can't get them some using a bucket (you MUST have at least one bucket). If there is a river or brook on the map (I always advise having a brook, not so much the river because of the carp), your dwarves will go there to get water, but sooner or later you will want an indoor water source, namely a well. The hard part is that building a well, especially one with running water (which dwarves will like more than stagnant water), requires understanding of both the z-axis and water pressure. The wiki article has additional details. A basic well design would look like this:
Code:
##### ^
#W |
# ### |
brook~~#~### |
######~#~### z axis
######~~~### |
############ |
W is the well tile, ~ is water, # is rock, and brook is a brook.
Building your well farther away from the brook just requires digging longer piping, so to speak. So you can build your well basically anywhere, as long as you keep in mind that even if water is led through lower levels it will "flow up", so to speak, due to water pressure. A mistake may flood half your fortress and kill your dwarves. We demand pictures.
combat thieves: Buy some dogs, manufacture or buy a rope, train them to be war dogs (this is as easy as giving a dwarf novice animal trainer, or giving any dwarf the animal trainer labor if you know how to, building a kennel, and training them in it), then build a "chains" building near the entrance (it will not obstruct caravan wagons), and chain them up. Thieves will not get past them, unless of course you have more than one entrance. If your problem is mandrills or rhesus macaques, war dogs are still the answer - they will try and fight them if they are nearby. However, they will follow their trainer unless you assign them to other dwarves as pets, so if you have a dwarf working near the entrance you should give the dogs to him.
If you don't have any dogs...
military: I start my military using the first immigrant wave. Usually I get a stock of four or six dwarves that somehow thought Fish Dissector or Soap Maker or something along those lines would be the perfect professions for a fledgling dwarven outpost. These guys make nice recruits. Organize them in squads using the military screen. An on-duty squad can be stationed near entrances to hopefully discover and defeat thieves, an off-duty squad will spar in your barracks and quickly become stronger. Of course, they should get some degree of weaponry. This is possible without a metalworking industry, to a degree. If your map has obsidian, obsidian short swords (requires one obsidian and one log) are an excellent weapon. Bone and wooden crossbows as well as bone and wooden bolts can also be manufactured, to get marksdwarves. Leather can be used to make leather armor and leather shields (though wood can also be used for shields, and turtle shells can be used to make helmets). You can also trade some weapons. Sooner or later though you will want metal weaponry and especially armor, since it is plain better. Even copper. This would take longer to explain, so I'll defer you to the wiki on this one