Yes, if you can dig out the Shimano tech doc for the FC-M410, it should list BB spindle length for 50mm (at least) chainline (I'm not sure why you're uncertain about this, as "recommended 118mm" implies you already have the tech doc). You'll want to make sure you get the correct crank arm length for your leg length (170mm or 175mm; 175mm seems to be by far the most common one). In the very unlikely case that you've got an E-type front derailleur mount,
you'll also want to make sure the BB is correctly sized for an E-type front-derailleur.

I'd certainly put in a new chain (8-speed; the SRAM ones have a master link included, unlike the Shimano chains), and a new cassette should be pretty cheap. If the current cassette is really worn, it'll be pretty obvious once you install the chain.