Yes, deleting the download in LW 5 will delete the incomplete file also & remove it from the download preferences. LW 5 does have less options than LW 4 did such as pausing, etc.

Sounds like the file you found in search results does not have 100% identical download hash & may be the same song or video but different conversion file if you know what I mean, not 100% identical. Else, the one in search results, that person's upload slots or bandwidth are full.

Might be worth increasing your download slots in LW's settings. ie: LW's menu bar, Tools -> Options -> Transfers, up & down settings.

The Fix Stalled / Try Again, options have limited abilities. A manual search is usually far more effective.

Searching for more sources as you have been doing is a very good idea. Searching as you did originally to find the file will hopefully find more sources & hopefully the identical file, not simply one with same name. Longer you leave LW on usually the better it behaves. So keep using that process of searching every now & again. People log on or off from LW all the time. Also your LW will change ultrapeers now & again so different results can be found due to the newer ultrapeer being connected to a different collection of peers & thus searches may branch out in other directions of the overall network.

Oh just noticed you are a pro user, that in itself should help for the outer searches, especially rarer material.
Tools -> Options -> Advanced -> Performance, hopefully none of those options are disabled, especially the OOB one.