I think we already know the answer to the second question. Braun, already disliked in many opposing towns, particularly Chicago, is likely to get vilified in most opponents' ballparks, especially Wrigley Field. Will it affect his performance? Most players can shut that kind of thing out. Over his career to date, there hasn't been much difference in his hitting in Milwaukee (.962 career OPS) and on the road (.915 career OPS).
Will being off PEDs (presuming he is) make a difference? Only time will tell. One thing that will be different -- Braun will be patrolling right field for the Brewers instead of left field, with the departure of Norichika Aoki, who was traded to the Kansas City Royals (for a well-known actor, apparently). Khris Davis (and it's good he spells his name with a "K" so we can tell him apart from Baltimore's Chris Davis), who showed prodigious power (11 home runs) in a 56-game trial after Braun's suspension, will take over in left.
Scooter Gennett is listed on the Brewers' depth chart as the starting second baseman ahead of Rickie Weeks, but that might be a battle won in spring training. Weeks had his 2013 season ruined by injury and poor performance, and he's now 31, so perhaps the Brewers want to try someone younger.
The other significant change for Milwaukee will be the addition of former Cub Matt Garza to their rotation. Garza was signed to an Edwin Jackson-esque four-year, $52 million contract (after turning down the Angels because he was on vacation -- really, Matt, really?), and the Brewers certainly expect Garza to provide more value for that money than Jackson has (so far, at least) to the Cubs.
The Cubs will play the Brewers in six separate series totalling 19 games this year. The series are spaced far enough apart that it's possible that Garza could face the Cubs in all six of them. If there's anything we have learned about Garza in his two and a half years as a Cub, it's that he's a poor fielder (and poor hitter, too; as a Cub he went 12-for-112 with 74 strikeouts). The Cubs need to bunt on Garza when they face him. A lot.
Milwaukee's season went down the drain last year due to injuries and the Braun suspension. This team has a fair amount of talent and it wouldn't surprise me to see them return to a winning year in 2014.
The Cubs first face the Brewers April 25-26-27 in Miller Park; the Brewers' first trip to Wrigley Field is a weekend set May 16-17-18.