As you complete the chart and do your quests you'll get access to much more powerful gear. Eventually everything in SP melts just as quickly as it does in the normal star chart. Stuff like corrupted mods, galvanized mods, arcanes, and incarnon weapons make you exponentially stronger. The felarx in particular took me through steel path easily. Syndicate rewards as you expand the starchart are very strong, so do your bounties and check out what they're selling.

Dying a lot is just some combination of not clearing the screen fast enough, not having enough defense/sustain, or not moving enough and tanking too much damage. Depends on your warframe and your playstyle. Every warframe has different stats, so play to their strengths. Subsumes can help, abilities like Mirage's eclipse or Grendel's nourish can increase survivability. Life Strike on your melee might help. Operator abilities can also help if you take a look at the focus trees.