As with almost any Marth matchup, the key is spacing. Always be cautious of where you are in comparison of Marth's sword and once you get inside, make sure you overwhelm with your speed, Double Jab to Grab, general tiltage etc, these are all god sends. Marth won't kill for a long time without a tipper, though probably still earlier then you. HOWEVER, Marth has a very gimpable recovery (especially for Shiek, she was designed to gimp Marth lol), standard F Air and B Air offstage are both great for pushing him out of DS linear recovery line. Tether edgehog is also fantastic (time the invincibility frames). F Tilt to U Smash as always kills very well but fully decaying F Tilt against Marth is difficult, gimping should still be your primary way of killing.
Shiek can only combo with F Tilt when appropriately decayed, otherwise the Marth will Dolphin Slash out (it's invincible frame 1-4 and hits frame 5), so finish your lock quickly, after two F Tilts usually with D Smash, N Air or U Tilt (Marth can actually DS out of the second hit of U Tilt but I very much doubt they are that frame perfect or react quickly enough). You can also test your opponent's DS patterns and then bait the DS for a free anything.
Abuse the **** out of needles. Marth doesn't have a projectile, you do. This normally isn't much of a problem for Marth thanks to his great manouverability and ability to cancel many projectiles with his sword, however he can use neither effectively in this matchup. Needles don't get cancelled by sword and Shiek has the pace to run away. Needle's also aren't exactly easy to see coming and shield, making them the perfect tool to mess up Marth's spaced tilt's and F Air walls and generally whenever he's far enough away that he can't reach you.
For your specific move problems:
Dash Attack: Shield it, Marth has to commit and it has punishable ending lag.
F Smash: It's range isn't anything special anymore, be very conscious of if you're in tipper position at kill percentages, otherwise it's punishable on shield and it can't kill for **** without the tipper.
D Throw to F Smash: DI appropriately and Airdodge, it's not a guaranteed follow up.
F Air: This move is always going to be a problem, it's a brilliant spacing aerial. However, I find Shiek's Dash Attack very useful against double jump F Air, intercepting between the two. Dashing Shield can also be great to mess up spacing. Needles should always be your primary response however, running away to needles deal very effectively with Marth's F Air spacing.
Marth still has an advantage in this matchup (60:40 IMO) due to his general ability to space with his range, however he isn't as effective at shutting down Shiek as with many characters due to her speed, it's a very winnable matchup.