Gloves will be overkill for the covers. Just thoroughly wash/dry your hands and work slowly with the covers. The paper is quite sturdy.
Postmarks of this era seldom had year dates, so the contents of the letters or notes made by the recipient (often called docketing), may enable you do determine dates for some of these. By 1850, envelopes were becoming more common (it looks like the grouping of 3 may just be envelopes), with the resultant separation of the letter from the postal markings making dating more challenging. Contents in the envelope era are often missing or placed back in the incorrect envelope.
The 5 and 10 cent rates indicate use after July 1, 1845, so highly unlikely there is anything in the "Republic" period. The best source for information on the markings is the "American Stampless Cover Catalog" found at the link here:
https://www.uspcs.org/resource-cent.../your-input/