Get an LVL beam sized at a competent building supply - it may wind up being two LVL's nailed or screwed together. Jack up the existing roof structure. I'd use at least two jacks (four would be better), one (or two) on either side of the old beam, out about 2', with a pair of 16' 2x8's sistered together on top of the jacks running parallel to the beam. This will spread out the load and should allow you to get the roof back up to the correct level, and flat. Any "swag" in a roof that close to flat will cause problems.
Remove the old beam completely. Build new supports in the walls at each end for the new beam - the end supports look totally inadequate in your pictures. Sister three or four or five 2x4's together to support the beam ends. Make a pocket at the top to set the beam into, with one 2x4 running on each side running to the top of the beam. Set the new beam into place, lower the roof structure down onto it. Check to make sure you have eliminated the "swag" in the roof. Individually shim the cross rafters if you haven't. Use some Simpson or USP clips to attach the existing cross rafters to the new beam. The diamond shaped ones should work nicely. Re-install angle bracing from the bottom of the new beam to the cross rafters. Simpson and USP make those too.
Lastly, fix the roof. Do a full tear-off of the old shingles. That roof is way too flat for shingles, that's asking for trouble. Check the sheathing for rot. If its been leaking for long, you're going to have to replace at least part of it. Place new felt paper (or synthetic underlayment, preferably) over the sheathing. Place 1x4 furring strips on top of the underlayment across the roof on 2' centers. Get the metal roofing of your choice, and screw it down with 1.25" screws that will go all the way through the furring strips into the sheathing. Trim it out properly, use foam closure strips where needed. The garage will then be over 100 years old before the roof needs attention again, and that will probably amount to a paint job on the metal.