"...I'm supposed to install the water pump straight into the engine block, then loosely attach the two nuts on the right..."

It sounds odd that you would use two nuts on the same side of the pump in order to hold the pump square up against the bottom of the head. If you look straight at the pump you should find that two holes are slightly elongated vertically, while the other three holes are round. It's the two elongated holes whose nuts are loosely installed and then snugged while prying upward on the pump. The two elongated holes should be on opposite sides of the pump as I best recall. You just snug those two fasteners enough (not fully torqued) to keep the pump from sliding down while the other three bolts are installed. I have had the best luck just coating the gasket with a very thin layer of axel grease, rather than gasket adhesive, so that the pump can slide upward without buckling/tearing the gasket.

Before you install the pump hang it on the engine with all five fasteners screwed in finger tight and then backed out a turn or two. Make sure you can then slide the pump all the way up against the underside of the head. If it won't slide all the way up figure out why. You may have to clean up one or more bolt holes with a rat tail file. Some of the pump castings are horribly messy!

Also, before installing the pump, make note of how far the O-rings extend above the pump's upper surface. Then after the pump is installed and tightened take a feeler gauge and measure the gap between pump and head to verify that the the O-rings have been substantially compressed. No sealant on the O-rings.

If the old bolts/studs aren't so deeply rusted that they appear to be weakened, then you should be OK to stick with them. Often times a 40 year old OE bolt is better than a brand new one from Ace Hardware, even if grade 8+.
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Current rides: 2005 Volvo S80 2.5T, 2003 Volvo V70 2.4NA, 1973 Volvo 1800ES (STILL not road worthy!)