R12Rules,
Okay have had a lot of practice with 5H60 thru 120s. Worked for a private owned grocery store chain in NoCal that speced their own machine rooms and used carrier(carlysle) exclusively. We would changed them out in the field and then ship them back to be rebuilt. To you questions:
1) We used an engine hoist to lift them, our installation shop had dollies made, thick plywood with casters, like piano dollies that we moved them around with. Usually we hoisted them up and dropped them on to the dollie to move them around.
2) As far as alignment, the coupling instructions give you your tolerances and it is aligned after it is bolted to the bed plate, after the suction and discharge headers are installed. You align the motor to the compressor. Most bedplates have alignement studs or atleast nuts welded on the motor end for this. As far as the compressor is concerned level is all that matters. If it is the same compressor on the same bedplate use the same shims on the compressor end only, since that should bring it back to level. After the coupling is installed. If it is a carlysle then it should be a spring pack coupling. Anyway mount the dial indicator on the motor hub and read the compressor hub. Be very patient. Their are 4 areas that need aligning 2 are done with a machinist rule. You can measure the distance between the hubs top/bottom and side to side to fix the cocked alignment (radial?). Do that first. Next for side to side off and up and down high/low(axial). Use new shims for that. Whoever is your carlysle parts house should have them. A shim kit is expensive though, I think however you can buy just different packs, as a matter of fact I remember buying them from Grainger too. Our company bought a roto-aligner (laser), man talk about sweet, it would tell you where and how much and as you adjusted it would change to you were inspec. Since you probably don't have one the dial indicator is your only bet. I never knew you could out source the alignment to a machinist, but if you've never done it you might be better off that route. It's not too difficult, but I was taught while in the navy years ago and took to it real well. I have met people that couldn't align to save their lives. Heck spend the money have the machinist do it and see if he'll show you then the next time you can do it yourself. Or if you have a dial indicator, try it first and see how it comes out. That coupling will eat it self if you are out and it will happen on the weekend in the middle of the night. Hope I shed some light on it.