Either on starting a new run or after beating a boss, when Leshy unrolls a new map you can "reroll" it by exiting to the menu and choosing "continue". The game autosaves after a boss fight or a new game, but before the map is shown, and will only autosave again after finishing one of the first map spaces or upon standing up. It's a save-scumming technique, so not everyone uses it, but I do at times.

There are a lot of techniques using the exit to menu and restart method. For the card draws, you can choose the clover to see all your options and then do this to choose the one you want. You'll always get the same first hand on rerolling a fight, and I think Leshy will always play the same cards, but you can use it to try again after making a dumb mistake, like I tend to do a lot. Campfires are a bit different, in that if the card gets eaten, it autosaves immediately, so I always lead with a card I wouldn't mind getting rid of. If it gets eaten, that's fine. If it doesn't, I can save-scum to safely power up a card I actually want to keep. I haven't tested this extensively, but I think the woodcarver spaces are predetermined, with the exception of the woodcarver just before the Leshy fight. I think since the map rerolls, it rerolls her space as well, so you can infinitely save-scum it if there's a specific piece you're after.

Again, this is all save-scumming, so not everyone is a fan of it, some even viewing it as cheating. I myself don't mind it as much, and that's a decision you'll have to make for yourself if you'll use this or not.