I have 7 light bulbs I want to power on with four switches. If it's not possible with this many light bulbs, you can redefine the parameters. I can provide more of a blueprint if needed. For example,

If switch 1 is interacted and it's connected lights are powered on, then switch 2 when interacted will power off any lights that it has in common with switch 1 and power on any that are connected to it that are powered off. It sounds complex but basically interacting with a switch either allows or hampers a series of bulbs within the entire set depending on whether the light is already on and connected to the switch at hand. (I.e sw1 powers b1, b3, before -- sw2 powers b1, b2, b5 sw3 powers b3, b7 etc.)

If you can define a circuit that has a solution in this manner that would be helpful. He solution should be simpler than the request for any body who has expertise in circuits such as this.

A hypothetical circuit looks like this:
Switch 1 toggles bulb 1, 3, 5
Switch 2 toggles b 2, 3, 7
Switch 3 toggles b 1, 4, 5, 7
Switch 4 toggles b 3, 6
If the switch is toggles the light bulbs are either in a state of true or false

We need to toggle the switches in whatever order is needed for all the lights to come on.
A hypothetical solution would be: switch 1, Switch 4, switch 3, switch 1, switch 2, switch 4, switch 1, switch 4, switch 3. This is not one that is guaranteed to work.

An even more complex version would include this:
I need to program a switch to power on it's light bulb(s) which powers on their light bulbs, power itself off without powering off the lights, and when toggled again power it's bulb(s), and by extension the bulb('s) bulbs, off. However I need another switch to then power off bulbs that are attached to said switch which will then power off any of the original switch's bulb set that are connected to the second bulb. This happens up to switch 4, and when those bulbs are toggled and the electrical circuits are defined in the proper manner, all bulbs become powered thus opening the treasure room.

What I need here is what switches toggle what light bulbs to true or false, and what light bulbs trigger what lightbulbs on when on and off when off. A good answer would include a working circuit and completeable solution to the puzzle.

Regarding the first problem you posed, the easiest way to do this is by programming a micro-processor to read the states of the 4 switches and provide power to 7 outputs depending on the state of each switch. However, you called this a "puzzle," which makes me wonder of you're actually trying to make this work using only simplemechanical switches? It would be possible to do this with mechanical switches alone, but only if it's acceptable to use custom-designed switches that can switch multiple inputs and outputs with each change of state. For example consider switch 1: it must control light 1 in conjunction with switch 3, it must control light 3 in conjunction with switches 2 and 4, and it must control light 5 in conjunction with switch 3. Each of these operations requires a 3-way switch at the switch 1 position (a 3-way switch is the type that allows control of a light from either of two separate locations, and is used for example at the top and bottom of a flight of stairs so you can turn the light on or off at either place). So you could design a "super" switch 1 that consists of a three independent three-way switches, all of which change state when you toggle the switch.

I don't understand your second scenario, where a bulb powers a bulb - you'll have to be clearer about how you want that to work.