My guess is that Ian Kinsler will return to the leadoff spot once he comes off the disabled list, with Zack Cozart slotting back in the middle of the order. Cozart has undoubtedly been productive in Kinsler's stead, going 9-for-29 (.310) with two home runs in six games as the leadoff man, but I think Kinsler remains the Angels' preferred option at the spot due to his mix of on-base skills and savviness as a baserunner.

Not really. Manager Mike Scioscia didn't label anyone the official closer last year, either, though his preferences emerged as the season wore on. Cam Bedrosian got most of the save opportunities at the beginning of the year before landing on the DL. Bud Norris then stepped into the role and held it until he hit a rough patch in late July. Richard Parker took over after that and ended the season as the Angels' preferred ninth-inning option.
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I think it will be more of the same in 2018. Parker was summoned to pitch in the Angels' first two save opportunities of the year, but he struggled in both appearances and had to be bailed out by Keynan Middleton on Sunday against the A's. Parker has strung together two scoreless outings since, but if he regresses, it could open the door for someone like Middleton to start getting looks in the ninth.

Garrett Richards, who is eligible for free agency at the end of the year, has said that he would be open to discussing an extension with the Angels, though the club has not yet approached him about one. Given his injury history and this offseason's glacial free-agent market, it's tricky to assess his value, but Richards clearly has the talent to be a No. 1 starter. If he pitches like he did in 2014, he could get paid like one.
Is there any chance we could see Ohtani having less off-days as the season progresses during key situations/a playoff push (eventually)?
-- Nolen L., Las Vegas, NV
Scioscia said during Spring Training that the Angels could compress their projected six-man rotation and have their starters go on a traditional five-day schedule toward the end of the season, but it's unclear how Shohei Ohtani would fit into that picture since he's currently pitching once a week. The Angels are carefully monitoring Ohtani's workload to make sure he doesn't overextend himself this season, so they tend to map things out based on how he's feeling on any given day. I don't think the Angels would ever put Ohtani at risk by not giving him adequate time to recover in between hitting and pitching, so it'll be interesting to see how they balance that down the stretch, assuming they're in the mix for a playoff spot.

Not unless Ohtani is pitching in a National League park. Scioscia explained that it's too much of a disadvantage to lose the designated hitter when Ohtani faces American League clubs. Since Ohtani would be in the lineup as a pitcher, the Angels would not be able to replace him with a DH later in the game, which would be problematic if Ohtani were knocked out early.

Yes.