I started recently, and I just left Citadel. I have a perfectly balanced team, my vanguard and Wrex and the girl with the mask. Is it normal that me or a team member can die very quickly? I have normal armor and upgrades and pretty much can't buy any better armor. Are there any healing moves I can get that having nothing to do with medi-gel? Am I supposed to use medi-gel often and is it replinishable in my ship? I'm just worried about using all of it then not being able to find more.
Also I'm playing on normal difficulty. Perhaps I'm just not good enough at the shooting parts? I use the shotgun and use throw and warp fairly often.
Mass Effect is an incredibly easy game on any difficulty... once you get the hang of it that is. Really though i think most do indeed have trouble when first starting out because it takes some getting used to. The biggest mistake early on is the feeling to play it like a typical third person shooter just because it looks like one. This is not run-n-gun.
1- Use cover. Later on when you characters are maxed out and you have the mechanics of the game down, cover isn't really needed. But before that though, using cover is the best way to minimize incoming damage. You can easily get your squadmates to take cover too with the "up" button on the d-pad. Just place the resulting arrow at a bottleneck between two pieces of cover (example, a doorway) and your squadmates will set up against cover on both sides.
2- Build up your best defensive skill early, Immunity and Barrier respectively. For classes without either, the closest thing is Electronics (passive shield boost) and though not nearly as good as the previously mentioned two, you'll need it to open stuff anyway.
3- Disable your foes. You're going to want to invest in group disables like Lift, Singularity, Decryption (Sabotage functions as a disable vs most synthetic enemies), and AI Hacking (i know it only hits one synthetic enemy but it can cause a distraction to its allies). Single target disables, like Throw, can be useful too, but not nearly as much as the AoE ones. Often early on, you can not disable everything, so disable what you can and then focus your fire on killing anything that isn't floating. You can focus your teammates fire with one of the side d-pad buttons (i forget which one it is at the moment, left or right).
4- When using biotics, never target a specific enemy. Some of the AoE biotics (Lift, Warp) have a weird glitch where if they are targetted on a specific enemy, nearby enemies won't be affected even if they are within range. Instead target the ground, ceiling, or wall near the group. Make sure Target Assist in your options is set to Low. When with this setting, sometimes it is hard to get the power not to auto-target an enemy when trying to place it near them. I found the way to undo that is to keep the power wheel open, turn your view around to an area with no enemies, select a self-buffing power, then with the power wheel open turn you view back to your enemies and try placing the original power you wanted to cast again. Repeat until you find a place to put it where it won't auto-lock on an enemy.
5- Equip Medical Exoskeleton Armor upgrades. This way your allies and yourself will heal when in cover (which you can duck behind when your shields are depleted). Not only that, but the higher level Med Exos reduce power cool-down, enabling you to disable enemies faster. You can buy quite a few off of the Doctor on the Citadel. Some are pricey but since there really isn't ever a need to spend money on anything else anyway (except if you happen upon Colossus or Predator H/M/L armors at vendors or if you ever want the overpowered Spectre weapons after getting the Rich achievement, though neither are a concern until late-game).
Also not investing in the proper talents as you progress can make the mid-game harder than usual. I could detail which should be raised when, but the point could be moot depending on how far you are already (since there's no re-speccing, once a point is placed it is there for good).
Oh and to answer your question, the only way to heal other than using Medi-gel is to equip Med Exo armor upgrades, other than the Soldier (Ashley) and Battlemaster (Wrex) class talents.
Also, your a Vanguard should use your Pistol when necessary too. Even if you just have it at talent level 6, with the rest of your weapon points being dumped into Shotguns, it is still an effective weapon at mid-long range. This is especially true if you haven't gotten the Vanguard's defenses (a good medium armor, at least advanced barrier, adrenaline burst, and maxed shock trooper) in place yet, which without would make it hard to stay in Shotgun range at all.
Simbacca's advice is solid. I'd also like to add that you can tell your followers to use their powers/abilities. I've saved my butt many times using a follower's abilities. The power wheel is your friend. Also, make sure your followers are using the appropriate weapons.
I stress the abilities because in this game, control of the battle is often key. Use cover to protect you and your squad, use abilities of the entire team to support each other, shut down opponents and limit the damage they can do.
And if you don't know already: unless you're a glutton for punishment, it's generally a bad thing to overload a Krogan's weapons. They'll beat an education into you.
I weep for the future.