Supposedly the matte proof coins, especially the gold proofs, from the early 20th century were not popular and many of them wound up entering circulation. Same for the early modern proofs in the 1930's. They cost just barely above face value and when times got hard it wasn't a big loss to spend them.
As for the second question after 1858 the Mint did make proof coins available to collectors on a regular basis. Usually you could get just whatever individual coins you wanted, and in some years they only sold them as sets. Costs were still very low, for example a minor coin set that had the one, Three Cent Nickel
and five cent nickel with a face value of 9 cents cost 12 cents. In 1883 the sold a set of all three nickels for that year, face value 15 cents cost 18 cents. A proof Seated dollar
with a face value of $1, and a metal value of $1.04, cost $1.08. At some times the proof coins were offered on a circular the Mint published. Most collectors simply contacted the mint and requested the proof coins including banknotes and/or postage stamps in payment.