IMO, you definitely want to import your Mass Effect 1 character into Mass Effect 2. All of the major choices that you made in Mass Effect 1 will be reflected.
For example, at one point you visit the council on the Citadel, and that plays out completely differently depending on whether or not the original council is still alive (same with the choice of who you nominated for the council, Anderson or Udina). The same goes for who you killed on Virmire (Ashley or Kaiden) and if Wrex is still alive.
The same is true for the side quests, to a lesser extent. However most of these only have the follow up in the form of an e-mail to your private terminal on the Normandy, but it's still cool to know that your choices had a lasting effect on the story.
If you had a love interest, it doesn't have a huge impact on Mass Effect 2. When you meet them, you share a brief kiss, but that's about it. You are free to have a new (different) love interest in Mass Effect 2, but apparently that will have some sort of impact in Mass Effect 3.
Bioware did an excellent job continuing the story you started in the first game. If you could make a choice in Mass Effect 1, it is reflected in Mass Effect 2.
As for importing characters, I'm not completely sure about this but I believe that you can import any play through for a given character (it's been a while since I imported my Mass Effect 1 characters). If you don't mind doing another Mass Effect 1 play through, I'd suggest starting again with your level 60 character (or whichever one you want to import), and make all of the decisions that you want to carry over to Mass Effect 2. You could always put the difficulty on easy to help things go faster.
If you want to know how a given quest affects Mass Effect 2, you can always check the Mass Effect Wiki.
If you don't import a Mass Effect 1 character, the game basically makes the big Mass Effect 1 choices for you. Also, some dialog that is present for an imported character is not present for a new character (mostly minor things, but some text wouldn't make sense if you didn't play the first game).
Finally, at the start of Mass Effect 2 you are able to change your class and physical appearance (don't worry, it makes sense in the context of the story). You can't change your sex or name, however.
Once you set foot on Ilos, there's no going back. You're unable to return to the Normandy, so what you've got is what you've got.
This is why the Romance video (if applicable) plays during the flight to Ilos, which Bioware mimic'd in the sequel with a similar point of no return.
That said, there's nothing earned from finding more Salarian medals. It doesn't carry forward to Mass Effect 2, and you don't even get any real acknowledgments that you've completed it. This might be one case where you have to look at your inner perfectionist, and get them to say, "Eh, close enough".
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From @Iszi 's comments I have to post what happened. Hope you do not run into the same.
I first tackled the outpost where you land on X57. It is right behind you when you land. So found the body of Mendel. And how he died brutally.
Till then there were no stations marked on my map.
Then I took out the Fusion gun ahead of where I landed. Then repaired the transmission tower. Then went and got C Hymes at Survey Station 1. Recognized her death as a result of an explosion.
At this point the game did not mark her body as found. Which is why my question in the first place. I kept going back to the same station to make the game change her status to found.
Last I found the last survey station where Montoya should have been. Found all the clues to his vehicle. And then concluded that I found Montoya. But at that point there is a marker on your map about Montoya's dead body. Unless you pick it up even C. Hymes's body does not register as picked.
This is the crucial point that the Wikia article missed.
I went through with the mission, let Balak live. And then Simon is like all Where are my engineers? I was able to answer about two them found. He said please maybe the last one might make it.
Picked Montoya's body and Mission Accomplished. :-)
In my first one I did it the other way. And I tend to rely on my journal entries a lot.