Well, you haven't had an ideal start but it's pretty common and fixable so don't worry about it too much- you might have to do a bit of extra work on it over the next few weeks though.
So, if I've counted right you've got 6 tiger barbs, 4 neon rainbows, 6 zebra danios, 8 cardinals and 1 algae eater (Crossocheilus reticulatus). Have I got that right? That's a hefty amount of fish in a small amount of time for such a new tank. I would suspect you've had a big ammonia spike and that's what's causing some of the problems. This happens when there is a sudden increase in ammonia- new fish added, a dead fish, food left to rot in the water can all cause this- and there isn't enough bacteria in the filter to cope with it.
Another problem I can foresee is that all these fish (with the exception of the fully grown cardinals) are going to get bigger. The algae eater is going to get too big for your tank, and needs to be in a group anyway so the easiest way to fix that problem is to return the fish to the shop.
I would think about returning some of the other fish too, that's a lot of livestock for a 130 litre tank. As a very rough guideline, just to give you an estimate of how many fish you can have, you should allow 1 gallon of water for each inch of fish (using adult sizes). Not including the algae eater, you've got a potential of 55 inches in a 28 gallon tank.
Your tank would be more manageable (and less work so more fun for you!) if you were to stock it more lightly. For sure, you can't fit any more in.
So, sorry it's bad news but if you set it up properly now then it'll be running like clockwork in a few months and you'll be able to relax a bit. Fish are meant to be relaxing 
As for the chilling fish, you can just add a bit of boiled water from the kettle to your bucket of clean water before you add it to the tank. Not too warm , just to raise it a couple of degrees from cold tap water. You could test it with a thermometer if you don't trust your elbow. Don't forget to dechlorinate!
Hope all that makes sense.