Are fumes from lead-free solder harmful?

Yes, solder fumes is the result of burning flux no matter if the solder contains lead or not. In fact no-lead solders often contain more flux. Combined with a higher temperature the fume volume will be likley even more. 

What equipment should I use to remove fumes from lead-free solder?

Table top fans or blowers may vent the fumes to your neighbor but do not remove the fumes. Tip extraction is prone to clogging especially if the volume of fumes increases.  Using exhaust arms and filter units with HEPA and carbon filtration will remove solder fumes.

What is the most common Lead free alloy, and at what temperature does it re-flow?

SAC Alloy which stands for Sn (Tin) Ag (Silver) Cu (Copper) SAC 387 = Sn 3.8% Ag 0.7%Cu the re-flow or liquidise state is 217 degrees.

You take the S from Sn the A from Ag and the C from Cu this gives you the name SAC = Tin Silver Copper. The 387 is the percentages of the metal that males up the total Alloy.