@nasfer I don't want to sound rude, but painter is not a "fast" deck. Albeit is combo, it takes 6 mana compared with the 4 mana of key+vault. Also the combo is stopped by creature removal, so it's worse on paper. And having to play 3 colors instead 2 (vault+key decks often are UB) can be a nuisance. So what does painter does better than vault decks? Synergy with painter, translated into REB and pyroblast (and sulfur elemental, if you ask me). So often I don't hurry into combo, play my trinkets, faydens, snapcasters and get into a nice position to activate grindstone. If my opponent is not prepared for the combo, I can win of nowhere. And if the opponent is too focused on stopping the combo, I can win slowly with critters, trying to maximize rebs.
Problems with paradoxical? Trinket mage + chalice in the side works wonderfully. Also I play sb trinisphere if I expect storm decks, and painters is not really annoyed with trinisphere in play. Not to speak about lots of natural counters against Paradoxical Outcome!
Against mud, it's always hard. There are lots of openers that no deck can safely overcome. Revoker is maybe the hardest card, followed by ballista. In my case I rely on magus to transform all its lands into mountains, the small creatures to match it's small creatures, I limit my misstep count and don't play fluster in the main. Post side I often play more sulfur elementals and try to have 1 elemental and 1 painter in play, killing revokers while being able to match most creatures (sulfur elemental gets to 4/1 with painter naming white, not a bad blocker if needed). Of course decks with lower creature ratio work worse against mud, but jvp with by force seem a good starting point.