I think that reading cards is a very personal matter. That is, if you draw those exact cards for that spread, and I draw an identical spread, the cards may be telling us different things. I believe once you build a relationship with a deck, and once you have a personal style, the cards you draw will reflect your knowledge base and skill level. I think every spread a Reader draws is partially a reflection of themselves, which is why I think that an outside view may be helpful, but a different reader can never reach the depths of understanding the original Reader could.
All that being said...
I do love two-card draws. I find them to be powerful, intuitive, and informative ways to read. When I do it, I see the two cards combined and read them as if they were one. It is a great way to read, and excellent practice because it is so quick.
If the Fool appears twice, it is likely that the Reader was drawing two cards, then putting both back in the deck. This isn't a bad way to do things, especially if you are only working with the Major Arcana and your card selection is limited. After all, someone may have the Fool for different aspects of their personality, so you would want to allow the card to show up true again. Having the same card come up more than once could be an easy way to see if someone is over- or under-balanced in an area. In this spread it seems like the Fool is a part of the person's core personality, so in order to grow, they need to embrace the Fool (perhaps by letting go and being passionate and wild).
Many people read with the cards influencing each other. My favorite way to do this is with the elemental dignities (the elements of the cards influence each other, along with the combined traditional meanings. It can add so much depth).
No part of a spread exists in isolation, so all the cards have a pull on each other, but exactly what that pull is depends on how the Reader interprets it.
In this case, the way I see it, the Emperor and Empress offer an interesting juxtaposition (feminine desires vs. masculine core) but I would not read them as changing each other, rather they are in conflict. I don't know, that's just how I see it.
I do not see the Star or the Sun influencing each other. Other readers might. For the most part, I look for opposites (Empress/Emperor, Fool/World, 10 Cups/10 Swords, et cetera), consider the elements (I believe this spread has an excess of Air, so perhaps the Querent is really over-thinking things lately), which cards are nearest to each other physically, and which cards have designated meanings that could overlap (so if this spread had a Soul and a Core category, I would consider the two to have some overlap, and their cards would influence each other). In this spread, I think the two cards in each category influence each other a great deal. The Sun and the Magician I see as being a powerful combination, representing a person of great charisma. The aspects of the sun are funneled through a specific type of person; the type of person indicates how those Sun aspects are displayed. If it were the Moon and Magician, the meaning of the Magician would shift. If it were the Sun and Heirophant, the meaning of the Sun would shift.
If you are hoping to get someone's interpretation of the entire spread, I will try to make this short. I seem to be making huge posts lately...
Power: I don't know what "power" means in this situation (maybe the source or manifestation of the Querent's personal power?), but I see the Sun and Magician together as being a person of great potential resourcefulness and skill, who channels the especially masculine, vital, and expansive attributes of the Sun. I would consider them to be highly charismatic and perhaps a little charming, as well as generally adaptable without needing to totally transmute who they are. They are the sort of person with a lot of "oomph" behind them.
Desire: The person is refusing to take part in a personal revelation that is upon them. In the back of their mind, they know that things need to change, but they are steadfastly refusing. Maybe that shift in perspective the Hanged Man brings is very scary, or hard to accept. Along side this, the Empress suggests the person may be 'nesting' or surrounding themselves with familiar things in order to avoid that change. Juxtaposed with the Emperor below, I suspect the person is rejecting their true personality for whatever reason and pretending to be the Empress when they are the Emperor.
Core: The person is, at their core, a strong independent type. They have masculine qualities such as expansive action and outward movement. They may be a good leader, but their wandering nature may prevent them from becoming ruler of a realm. They may need to 'go places' or always be on an adventure in order to be happy. The Emperor comes off as stern, but the Fool suggests this person is not stoic. Rather, they eagerly seek experience and knowledge; they want to know what the world has in store for them. They want to be who they are in an exciting world, they want to take the leap and just do what their heart tells them.
Growth: At this current point in time, the Querent needs to allow themselves to become passionate about something in order to grow. This may literally be a lover [The Empress and Emperor juxtaposition makes me feel this spread may be about a homosexual or a transsexual, or someone stuffed in to a traditional gender role, or any place in society, that does not truly represent them], but it may actually be embracing some closed-off part of themselves they have been denying. The Fool suggests it is time to strip away some of that world-weary cynicism and go back to your innocent roots. When we go back to square one, what does the Querent feel passionately about? Where does their heart take them? That is what the Querent should explore in order to grow, and they should approach that passion honestly and fairly with a healthy dose of optimism.
Lucky: I imagine that these are the cards the Querent can always 'bet on'. The Star primarily represents to me the promise of hope. It may be far off, but when you're flat on your back you can always see the light above you, reminding you that better things are out there. Together with Strength, the Querent can always bet that if they look towards the future, their inner strength will never fail them, and they can achieve any goal. The Querent may also be the sort of person that, when they recognize their own inner strength, can always see hope for the future. So even if the Querent is not feeling particularly confident, they can bet on the Star and Strength to get them through. More practically, the Querent may find better luck when betting on long-term projects; 'quick fixes' may never come through very well for them. When choosing sides, the Querent may be better off picking strength (physically or of character) instead of wit, cunning, or skill. The Querent may get along better with people who represent a strength of will rather than cunning of character [let us reflect that the Querent's power cards represent a great magnitude of inner strength].
I'm not sure what you're looking for, but I hope this helps!
Oh, to answer your last question: I think the Querent is a person of great potential power (maybe not magically, but just personal power) who right now is shut up in a corner that they can't get out of or don't want to leave. They are denying their true nature for whatever reason, maybe because to be true to themselves requires a scary leap of faith that is hard to take. They are the sort of person that wants to live life and find adventure. They like being in control, and they are really good at that, but they are not domineering. They may be having gender or sexuality issues, or for some reason they are repressing the masculine part of their personality (Eh, they could even be staying with the wife when what they really want is to cut free and go on the road... there are a lot of possibilities here). For some reason they strike me as being generally honest, with a strong desire for independence. Life turns out best for them when they go in it for the long haul and trust character over cunning.
This was a fun spread to try and figure out... I may have to try it for myself some time