Are you content with Jose Molina as the primary catcher for the rest of the season? If not, what are the alternatives?
Yes. But that doesn't mean I wouldn't welcome an upgrade at the plate. The Rays didn't sign him expecting a repeat of his 2011 performance. I went into the season expecting he'd continue to play above average defense and hoped his OBP would be above .300. So far he's done one of those two. Unless his offense REALLY goes into the toilet no one is replacing him as the primary backstop. It's possible the Rays add more catching help, since their two primary backups (Jose Lobaton and Robinson Chirinos) are injured, but likely wouldn't give up what it would take to acquire an impact bat.
How will the Rays try to compensate for the loss of Evan Longoria?
They're going to use some combination of Elliot Johnson, Jeff Keppinger, Will Rhymes and Sean Rodriguez. Obviously that won't replace the value Longoria brings, with the bat or the glove, but they should be able to be replacement level in his absence. He was out a month last season and they were able to play pretty well. The offense is better this season with the additions of Carlos Pena and Luke Scott, so that helps to soften the blow.
It's too early to get worried about any reliever. Each of the guys you mention have only thrown 12 innings. Peralta had a rough start to the season, but has rebounded of late. His ERA may be ugly (5.68) but his FIP (3.51) and xFIP (2.75) are excellent. His K/9 is over 12. He's fine. Badenhop's numbers are a tad bit uglier. His groundball rate is down to just 50 percent after averaging ~57 percent the past two years. Watching him, it seems to me that his fastball isn't sinking like it should. If his numbers look the same at 25-30 innings, then I'll start to worry.
How do you see this series playing out?
It should be a good series, with the marquee match-up being Price vs Sabathia on Thursday. Even if the Yankees haven't played that great to this point they still scare the hell out of me at home. To me, they're still the best two teams in the division, Baltimore's hot start be damned. If Shields can keep the ball in the park, the Rays have a good shot of taking the first game. After that it's a crap shoot with Niemann vs Phelps and Price vs Sabathia.