What is going on?!?!

I am sick of this. I am confused and need some help. My tank recently cycled (it's a 29 gallon), and I finally got to stock it. Before the tank finished cycling, inexperienced me decided to add fish (about 3 weeks ago). I started off with 4 corys and 6 amano shrimp. Luckily all the amanos made it, but sadly I now only have 2 corys. I did not blame my LFS i bought them from because I knew it was my fault. I have learned a lot since I first decided to get a bigger tank. Well now I could finally add fish safely, and I started with 2 red wag platys from petco (Look at my profile for the post on them). One died within a day, the other within 3. I thought it was petco's fault, but i tested the parameters. Came clean with 0 ammonia and nitrite, 10> Nitrate, PH 7.4, Temp 75.5. Then 1 week later, I whent to the LFS again to get about 8 cardinal tetras. I was excited to at least finally have some colorful fish in the tank. The first one died within an hour, I have to say something about this one though. He was about 2 inches (No idea how), and he swam very weirdly (swam to top{on side sometimes}, then floated to bottom). Then 3 died today when I got home (they were fine in the morning, except one was at surface not moving much). I tested my parameters about 10 minutes ago, they were the same as I had previously told (0 ammon. and nitrites- 10> Nitrates, PH 7.4, Temp. 76). One of the thing I must tell you is my tank recently had an algae bloom. I purchased the aa Green killing machine 4 days ago. The water cleared up since, but not yet fully clear. I am telling you this because I am confused as to how the possibility(if there is one) of parasites exists. The remaining 4 cardinals are doing ok (i think). BUT... 2 have this weird dorsal fin... PICS. The reason I write this is because all new fish I put in die. The corys and amanos are happy. I am thinking it's the store, but I would like opinions.
NOTE: I do acclimate the fish. I have live plants and aquaclear 50. I do a 20-40% water change every week. I dose with flourish. I am planning to get a fluval 306 to triple my turnover rate.
What can I do to keep the fish alive and much less, thriving? I am frustrated seeingothers have success and simplicity on their first try (no problems and perfect water, fish, plants, etc.), while my tank seems like a mess. So to conclude, sorry for posting so much (some of you might remember my other threads) and for ranting.

Thanks for your help

PICS

I used Dr. Tim's One and only, and I think I'm answering your question as my Nitrogen source were the corys.

No I did not quarantine them. I cant exactly set up another tank, and invest more money into another small tank.

The cardinal acted normal as far as I know. About 20 in a 55g tank. I must point out that the LFS is extremely helpful, and I don't think they would purposely sell sick fish.

I put the bag in the tank for about 30 min for a temp acclimation. The I transfer them to a bucket where I run airline tubing to drip tank water into the bucket until the starting amount of water is doubled.

UPDATE: Another Cardinal died... One of the ones with white dorsal fins. About 20 minutes ago he was at surface A LOT.

Thanks for all the feedback! I did lose another cardinal (the last one with white fin). I have 2 left and they seem to be doing fine.

To OrQidz and FishFan Man - I will be going back to the LFS to get a refund because they offer a return if the parameters are stable. I will ask them about the TDS and get some more plants. When I go, what are some good, tall, stringy plants (I have a finnex fugeray planted+ 30") that are medium-high light? I use Flourish and Excel (I have reduced using Excel and only use it in small amounts)(I also have flourish tabs too). I put in an airstone to get more oxygen, and I dechlorinate with prime. I do use a drip system as described in my last reply.

Thanks again for the replies, it means a lot.

Maybe bad stock but most likely not. Definitely not improper cycling. And I can't think of anything that would contaminate the tank.