I see you went with Flaming Hands. That's not a bad mutation by any means, it does have some advantages, it's just not nearly as good as Freezing Hands. Not only does Freezing Hands do damage, it freezes your enemies solid so they can't fight back. So freeze them and walk up and start whacking on them. After you get some levels you can keep most enemies perma-frozen with the short 10 turn cooldown it has. Plus, it shoots in a ray, so you can line enemies up and freeze 2 or 3 at a time. I can't emphasize enough how useful this all is.
Second, never, NEVER head directly to Red Rock for the first quest without getting 4 or 5 levels first. It may seem like that's what you are supposed to do but it isn't. You need to wander around the areas outside of Joppa first leveling up. This is why you aren't surviving past Red Rock. Avoiding doing this quest too soon is very important to your survival. Seek out the snapjaws in the zones around Joppa and kill them, they are easy and drop a lot of good starting equipment. At the very least, walk the zones to Red Rock rather than using the overland map.
Always check the 3 chests in town that you can loot without anyone seeing you (close the doors). If you're lucky you'll get a bow and 2 artifacts and maybe some other decent starting gear and food. Make sure you equip and use a bow or gun ASAP (always buy all the ammo at the vendor, it's cheap). If you get an artifact, take it to the Tinker in the building on your bottom left and turn it in to complete his first quest. That's a quick 75 XP. If you got 2 of them in the chests, then turn in the second one as well and complete his second quest. That will bring you to level 2 without leaving town at all.
Talk to the Zealot in town and get his quest to visit the Six Day Stilt. Then kill him and take his book. Don't worry, everyone in town hates him and the book sells for a decent amount. Plus, he's worth a few XP.
On the upper right of town, use "look" to examine the statue there. This will give you a quest to visit a nearby historical site, which often has many goodies you will want and sometime a relic. Plus you get XP when you arrive there for finding it.
Later on, make sure you get the Tinker Examine skill which will help you identify artifacts. Most of the good equipment in the game you'll want are artifacts until identified so think of this as a permanent scroll of identify. At the beginning though concentrate of skills that have a big impact on your survival. You start with Long Blades skills so maybe Swipe and Mighty Swipe would be useful.
If you have a buckler, it gets equipped on your arm, not your hand so you can still dual wield with a buckler equipped. A normal shield has a higher defense rating but occupies a hand slot so you can only use one weapon. Something to consider.