A plumber could have dealt with the toilet issue. In a newer house, there are some fairly reliable DIY-type ways to deal with the tile, also. In a house as old as that, assuming the plumbing and that toilet go "way back" it could be not DIY friendly.
What happened with the grout??
With a tile saw, a round carbide tile blade for a hack saw, and nippers, you can successfully cut tiles to fit closely around the toilet. We always recommend lifting the toilet, but at this point that may or may not be an option for you.
For the best help with your grout issues, consult the tile experts at this forum: www.johnbridge.com
We would like to see some pictures, and could advise on the toilet issue.