First off, I would just like to say that I would sell my own soul to see a team run that top-4. That would be absurdly fun.
That said:
Both Karlsson and Carlson are probably gonna cost about 2 million more than you've given them. Not a huge deal, but it's there.
You have 11 million in cap space and your 3RW didn't see the NHL last year. Re-sign Neal.
That Carlson contract's gonna look ugly down the stretch. This is true about basically any Carlson contract, since it's gonna be big money and big term for a guy who's already had most of his prime.
I don't see why Vegas wants Carlson. It's an inevitable bad contract, and they don't need him. They've got a decent 1RD in McNabb, another potential 1RD in Miller (top 30 in the league's dmen in GAR), and plenty of offensively gifted dmen (Schmidt, Theodore, Miller). Miller in particular has the potential to evolve into Carlson without the inevitable awful contract. The team doesn't need to make a big signing just to make a big signing. Keeping the group together while making minor upgrades is enough, given that this team won the Pacific and made the Cup Finals this year.

that contract would go till hes 35. it would be a bad contract for maybe a year or 2, but based on his play in the cup finals and the regular season Carlson is worth every penny

Carlson is worth that money now, but Vegas can get #1D play for less out of Schmidt, so it's not worth every penny to them, especially on an actual Carlson deal, which is more like $10 million. Also, I think you're underestimating how fast guys decline after 30. That probably starts being a bad contract around the time he's 30, it's #1Dman money for a decent 1RD/strong 2RD by 32, and it starts hitting unworkable territory around his age 33 year, if Carlson ages like most players. Given that it's not an incredible deal at the start (10 million to Carlson is about what he's worth), that's not a great contract to have. IMO the team that signs Carlson should do it because they need a #1D and an offensive 1RD, and this is the only way to get it. Vegas doesn't need him, so they don't need to screw themselves long term by signing him.

Do the other trades make sense?

hes not making 10 mill for 7 or 8 years, what kind of weed are you smoking? Erik Karlsson is making that much, not John Carlson. hes getting 8 mill 7 years or so. also NHL players keep themselves in prime shape, the way fitness and training has developed players can play till 40 easily (not being worth 8mill but still). Luongo is 38 years old and still a solid started. Ryan suter is still playing great hockey and hes 33. also read what i said, i was saying he would be worth his contract, i didnt mention the VGK thats a different debate

i dont see why trading eakin, hes a solid depth guy for you guys, and doesnt make an insane amount. also its not like the VGK have cap issues

Matt Cane has him at 8.5 million for 8 years, and his model tends to underestimate high-end guys. I've heard 10 million floated around frequently in the twitterverse. EK probably will make that much when he hits free agency. Very few players play till 40, with most bottoming out in their eary-to-mid thirties. Luongo and Suter are not the norm (also, goalies tend to age better than skaters, owing to speed's lesser importance in net). Most players start to hit the wall at 30. Bobby Ryan's 31 and went from top-six scorer to a guy who should be a 4LW on a good team last year. Loui Eriksson's 32 and age has already killed his scoring. Carlson's next deal could easily end up like one of them. Also, If Carlson isn't necessarily worth it for Vegas, why does Vegas get him?

i dont think vegas should get him, like i said i was arguing how he was worth his dollar, and i guess its a wait and see about him, i think maybe the last 2 years of him contract he might not be worth it.

Carlson is projected to go for around $8.5M. He's not going to pull more than that regardless of where he goes. DC has a huge income tax, so they have to offer more to really compete. Nevada has a lot of tax advantages that make the real value of that contract higher as well, so Vegas or one of the Florida teams might be able to get a bit of a discount (no state income tax).

I'm really split on paying a 28-year-old guy that kind of money for 7 years. While I think he's worth it now, there's no guarantee that he ages well.