1. You can use Perfect World DF, which uses random noise (or images, having been used to create earth copies for instance) for the painting - then adjust the few squares you desire to adjust.
2. You can often (though not always) change available soils and minerals in an embark without changing general layout by doing a large change in volcanism somewhere. (Mineral scarcity doesn't affect soils.)
Aquifers are strongly dependent on elevation - world with flat 299 painted height and world with flat 100 painted height will be somewhat similar, but the second one will have massive amount of aquifers, while the first will not. Of course, stone aquifers will only occur in sedimentary layers, and soil aquifers can't occur in clay - so you can create spots where there aren't any at all elevations.
Rivers flow from mountainside to lower as result of high rainfalls. This can be used to direct them
like this. You can thus direct lakes to pool into grasslands/deserts (though deserts have any real rainfall of their own.)
Also, at 100-103z elevation rivers won't be generated on their own, thus also preventing lakes and oceans taking bites out of areas. Overall, the river formation with flat areas is bit erratic up to 118z in my experience. However, properly constrained - such as 104z strip of land surrounded by ocean on both sides - they'll be pretty predictably follow the direction of the land as minor river or brook.
Brooks, of course, are the smallest rivers, so decrease rainfall/mountainslopes enough to change things in an area and generate again.
(In general, lakes tend to pool on the mountainsides and edges of world, especially if you provide river support to those areas.)
Of course, specific location of the river is still pretty random at local level. You can tilt them a bit with minor changes sometimes, such as by adding a cave, which tends to change local geography more than rivers. To my knowledge, this is the extent of the change you can do without getting completely differently named rivers.
3. High volcanism areas have magma pools in caverns as more common. As long as there's no volcano the geology is unaffected - the surface of 0 and 100 volcanism embarks look the same, ignoring differing soils and plants.
5. To add to what PatrickLundall said, you can turn off oreographic preciptation to have your region be more like you painted - though it is better if it is a little larger than minimum for medium and large areas, as lakes and volcanoes can break it up.
Few tricks: all flat adjoined plains are counted as 1 region, and so are hilly ones, but hilly and flat plains are considered as different regions.
Elves won't settle on taiga, but they're considered part of a forest region.
0 savagery area with 100 savagery in 7 tile radius will put goblins into that 1 square and constrain them to it for over a millennia, provided they can't conquer another site of different civ.