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Have you looked at the local building codes to find out what is required for a foundation and footing? Soil conditions, depth of the water table, depth of the frost line, loading and so forth all play a roll in what size footing you will need. Your best bet may be to have an engineer look at your site and design a footing for you.
As for laying it out, square and level are the most important things. The level part can be done easily enough with a transit or a construction level - you can rent them at many tool rental places. If you are careful it can also be done with a string and a line level but I wouldn't advise it. As for squaring the foundation, you can do that with a transit or even with a long steel tape measure and some simple geometry (3-4-5 triangles are always square). Here again, an engineer or a surveyor may be less aggravation in the long run.
Being that you are building a house on this foundation, you probably want to get it perfect. Might not be the best project to learn how to do this...especially if it is your own house.
To me stem wall is a seamless combined wall with slab.
A Stub wall is a wall of any height up to say 4 ft that is poured on top of a footing then later could be back filled on one of both sides
or
back-filled on one side and concrete floor on the other with walls of a structure constructed on this concrete wall.
For a level I have used the old fashioned garden hose with a clear piece of tubing on each end. Just mark the water level on both ends at the bottom of the meniscus and measure as appropriate from them, -it is dead on accurate. You can measure level at one foot or 500'+, just as long as you have enuf hose...
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