Sounds like ich is the issue. The guppy probably died from nitrate toxicity (as too much can kill just as ammonia and nitrites, but it would have to be a very high ppm unless the guppy had an already weakened immune system).
Ich meds will have a good chance of killing the shrimp, but them again, the shrimp can be removed from the tank while you treat it, as I dont think ich can live on shrimp (dont quote me on that, as I am not positive).
Yeah, you can bump up the temp and add aquarium salt. Or you can use the ich meds (remember to take out the carbon filter during treatment if you have one...and to put a new active carbon insert in after the treatment to remove any access meds, then do a partial water change, check the water parameters). I have seen ich clear up in 3 days before.
Ich can be introduced from new fish, yes. It can also develope in low water temps, and in stressed fish with weakened immune systems.
Personally, with the 6 fish you mentioned in a 10 gallon, I dont think you are overstocked. Personally it comes down to the swim room needs and bioload...and your fish dont seem like it would be an issue in the 10 gallon. I have 4 guppies, a balloon molly, and an ADF in a FIVE gallon tank...and yes technically it is overcrowded, but with proper water care they are thriving...despite this, I am upgrading the tank for the sole purpose of being able to add a couple more guppies. lol. When it comes to people's definitions of overstocked, I think it comes right down to personal opinion if there isnt anything wrong with the fish, and 6 fish of that size in that size tank with the water changes and such you have mentioned seems absolutely fine to me.
Yes, it is recommended to quarentine new fish. Something I wish I had the ability to do, but I dont generally keep a spare tank set up for this...I just add my fish as normal. It isnt always an option for everyone, and I have been very lucky as not to have any issues regarding this, yet. And when the issues happen they will be treated as needed. Everyone fishkeeps in their own way...and you did right by asking for advice and opinions.
As far as the nitrates go... if you have the ability to add an additional bio bag to your filter, I would do so, and in it put in one of the filtration medias from Fluval that help remove access nitrates, nitrites, ammonia, and other dangerous things in the tank. The cheapest and most effective way is to do your water changes when levels are high. You can also get an item called "Correct pH" at Walmart by Jungle for just over $3 that will help break down the ammonia, level out pH, and just keep the water parameters at a stable setting for 3-4 weeks per dose. I use it, it works great, and dont know what I would do with out it, especially at the price.
I know it has been well over a week since you posted this, and I am sure you have everything in order by now. But I wanted to give you my 2 cents...especially since there seemed to be some tension regarding the thought that you were overstocked in your tank. Like I said before, I am overstocked in both of my tanks, but you wouldnt know it because of proper tank care. And I FULLY believe that fishkeeping truely is a matter of opinion and personal experiance...we all learn and adapt to what works for us.
Hope all your fish are better and you havent experianced any additional fish loss.