Welcome SheDee:
If your floor joists are spaced at 24" on center, you may want to consider another joist centered between the existing ones. Yes, joist hangers are the best way to install them.
For the sagging floors, a new 4 X 6 beam centered under the existing joists and perpendicular to them, blocked up every 4' by digging down to bearing dirt and stacking concrete blocks to hold them. With the new beam at midpoints you may not need new joists.
Glenn
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