How to save up elixir for upgrade

As long as you attack the resources you will get them. What many people do is use army compositions such as Barch (barbarians and archers), GiBarch (giants, barbarians, and archers), or BAM (barbarians, archers, and minions (these armies only take 15-20 minutes to train so you can attack up to 4 times in an hour). If you go to low gold-high silver league and attack bases with high available loot (somewhere above 200k gold and elixir). In about an hour of raiding with these armies (without boosts), I can gain anywhere between 750,000 and 1,500,000 gold and elixir and a few thousand dark elixir.

Another tip is to leave your TH outside so people "snipe" it for trophies. It will give you a 12 hour shield and make it so people can't attack you for a cheap price of just a few trophies.

When you are attacking, don't worry about winning raids and keeping up your trophies. Since you want to be staying in a range anyways, going too high will just cause you to need to drop trophies again.

In response to your final question, the reason behind gaining trophies is to try to get to the top of the leaderboards and get league bonuses. You can also get gems from achievements for trophy pushing. When raiding for loot, there is no reason to worry about leaderboards/league bonuses, just go wherever you can find the most loot.

Been awhile since I've played some Clash but I'll try my best.

Raiding

When someone raids and attacks those resource tanks or the storages they receive a percentage of the values inside. Here is a pretty good list:

Table Link and More Important Raid Info!

It shows that the higher level you are the less percentage you get. Also if the town hall attacking you is a higher level they receive even less. But they will still get the resources they attack and get, regardless of the star count. There is just a limit to how much they can get.

So in my opinion, because it's one of those games, I would recommend taking advantage of that 8 hour shield and putting the elixir storages in the most protected part of your base. All my opinion, I'm not a pro and probably never will be. Good luck!

In order to save elixir, you use 18 ballons level 5-6 , 2 dragons and 35 minions to save even more elixir,gold and dark elixir

Well, it depends actually. If you are a town hall 7 trying to unlock dragons, I suggest you wait till you are about midway before getting dragons. If you are a town hall 8, I suggest you take your time as in this level, you will be having an abundance of elixir while you run low on the other resources. I don't suggest that you stop raiding as that is your main source of income at th7+ . You could use a barch army with rage or no spells. If you have lots of space, I suggest having a slight bit more archers than barbarians. Also try dropping or staying in silver 2 as most people there are either dead bases or are bases that are upgrading. Stars are just like checkpoints, without the respawns. It shows you that you achieved a certain part of the raid. People mostly raid as they want to reach higher leagues for better loot but you could stay in gold 2 or 1. People who raid you do keep their resources that were raided even though they lose, but you get a small portion back by the loot cart. Also don't let people snipe your town hall as after the update, resources are stored there too.

look guys use 75% Archers and 25% barbarians. And take 2-3 healing spells and destroy all the resources target for th 7-8 players they have the max lvl resources raid dont worry about elixers and later u can push when all purchase is completed

I managed to stock up 7 million of elixir in 4 days to upgrade my pekka to level 4 by using mostly dark barrack troops. This eliminates any expenditure of elixir (except for the spells) and saves up elixir faster. I used 16 hog, 10 valkyrie, 8 wizard(level 4-7), 4 wall breakers(level 4-6)(Total cost=1340-3740 dark elixir & 34000-50000 elixir)(excluding spell)

The same can be done in case of dark elixir by using mostly elixir based units. I managed to save 70k dark elixir to upgrade my hound.