Specific Growbox Questions

I am a first time grower and recently purchased a Homebox S with dimensions of 2.6'x2.6'x5.3' (LxWxH).I have been doing a lot of research on lighting and ventilation but wanted to ask some questions to see if my thinking is correct.

1. For a space this size, i plan on getting 4 clones and growing them fully in this box. Would that amount of plants work for a box this size?

Lighting: I am planning on using CFL's for vegging and a HPS system for flowering.

2. How many CFL's should I use, and at what wattage, would be good for this setup?

3. Also, I am planning on using a 400W HPS system with a hood that allows ventilation through it. Would a 400W HPS work for a box this size?

Ventilation:I am planning on getting a 200-250 cfm inline fan for exhaust, and a 50-100 cfm inline fan for active intake. Both of these fan would be mounted inside of 4" insulated ductwork.

4. Would having a 200-250 cfm inline exhaust fan be overkill for a room of only 36.2 cubic feet? Or will this size be good to help expel the heat caused by the HPS system i am planning on putting in?

5. I have heard you want your exhaust fan to be 2-4 times stronger than your intake fan to create negative pressure, or whatever the term is called, is this correct?

6. What cfm rated fan would u buy for a intake and exhaust in a setup like this?

Carbon Filter: Since I am growing in an apartment, a carbon filter is a must. I plan on either building or buying one.

6. If i was to buy a carbon filter, does my exhaust fan choice have any bearing on what filter i should buy?

7. Which is better, mounting the filter inside the box, and pulling the air through it with the fan, or mounting the filter outside the box, and pushing air through it?

I appreciated any help you guys can be in helping me out with these questions. I just want to make sure all my calculations and everything are correct before i go out and start spending money on this stuff.

-J