Hey,
Generally, it takes about 5 weeks of healthy growth under good lighting to have a plant ready to flower, if growing it from seed. If you run your lights 18/6, they'll pre flower as soon as they're mature.
As for your 2nd question, 'these' plants all depend on the strain you're growing for their mature height. Within a strain, you have different phenotypes, so that means all White Widow females (for example) won't look or grow the same. Jack Herrer strain has 4 different phenos, only one of which is short, indica like. With the hybridization of cannabis, you have indica x with sativa, and then the final product is marketed as a 'strain'. To the point, you're always going to have sativa traits (tall and stretchy) showing up in viturally every contemporary strain. (this is also why hermaphrodism is so prevalent in cannabis)
To be sure, there are plenty of phenos that will fit in a small area like you describe, have dense growth, good yields, and potency. It would be nice if you had a more open area for the selection process and could then do your final growing in that 3' spot. Also, consider the ventilation needs.
Edit: The above post came in as I was typing this, and I would say that this is a typical height for many plant types. Nice plants too.