Infect can be a tricky matchup, they'll have clutch counters and can present a legitimate risk early while maintaining late game presence with the difficult to remove Inkmoth Nexus. In your specific situation, I'd have to agree that Tidespout Tyrant offers the best opportunity to win. Assuming he doesn't have any pump spell, you're able to block 1 of the Inkmoth and go to 9 infect, then on your turn hopefully draw some gas to bounce the blighted on the next swing and still be able to block the second Inkmoth. Issue being, as the Infect player, I'd hold off until I draw some pump, knowing you're on the defensive, and try and get in with at least one creature to boost to lethal. At that point trying to swing the Inkmoths into your blocker wouldn't be my first choice. If Infect is big there you could consider either
Blazing Archon as a sideboard option.
Against Storm, I don't agree on your Thoughtseize target, you're leaving him with a minimum of 6 mana plus the tutor, taking the cabal therapy is borderline beneficial because now he's one step closer to a natural hellbent. Sure leaving him with it means you get your Exhume nailed on his turn, but most likely, that will be the extent of him turn and you have the Ponder to find the other 8 effects in the deck. Taking the Infernal Tutor leaves him with only mana in his hand, which is very very dangerous, but much better than mana plus something to do with it. Game 2 I can agree that your starting 7 isn't the best, but it's pretty good against Storm. They can be just as fast as you, but less resilient. Crippling their hand early should buy you enough time to have better draws going forward and assemble your combo first. Landing three discard by the second turn ensures that easily, and you're just a Brainstorm or a Ponder away from being right back to where you want to be, while they're trying to regain critical mass.