Jtdcftul

According to the PHB/basic rules, "Weapons and armor used by monsters are rarely in good enough condition to sell."

Are nonmagical weapons and armor used by monsters in good enough condition for PCs to equip and use themselves?

This statement is mostly there to prevent ludicrous amounts of not-very-useful loot being distributed for every goblin or bandit in the game. It's a guideline rather than a rule, what loot is available (and what condition it is in) is ultimately up to the DM, but it's just kind of a waste of time to end up with 23 long swords, 14 short bows and 35 hide armors every time you run through a bandit stronghold. It'd also increase the gold value of an average humanoids loot quite significantly if all their equipment was PC-grade weapons and armors, although I'm not sure how much of a problem this is in comparison with all the micro management that'd have to happen in this situation.

As a rule, yes. If it fits

The section you quote is specifically about selling equipment that you find (PHB, p. 144)

Selling Treasure

Arms, Armor, and Other Equipment. A s a general rule, undamaged
weapons, armor, and other equipment fetch half their cost when sold in
a market. Weapons and armor used by monsters are rarely in good enough
condition to sell.

Rules for using equipment you find are found other places. Some significant rules are found in the following section on Equipment Sizes (PHB, p. 144, bold added).

Variant:Equipment Sizes

In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling’s
leather armor, and a gnome would be swallowed up in a cloud giant’s
elegant robe.

The DM can impose more realism. For example, a suit of
plate armor made for one human might not fit another one without
significant alterations, and a guard’s uniform might be visibly
ill-fitting when an adventurer tries to wear it as a disguise.

So most of the time, if you find equipment and it is reasonable for you to use it, you can. A DM is the final judge of what would be "reasonable" to use. Note that this decision could be based on something other than a creature's size. For example, a bow made for an Illithid could have a grip too alien and strange to be comfortably used by a humanoid. Also, whether or not equipment has been damaged may be a factor. A DM might decide that armor worn by Orks is usable if they were disabled by a sleep spell, but not if they were killed by a might blow from a warhammer. Armor that usually would fit might become too dented to be worn after you kill its occupant (although a DM might then have to bend over backwards to explain why your own armor is wearable after you've succeeded on three death saving throws).

However, some DMs may ignore any of these concerns and declare that every piece of equipment you find can be used by you. It all comes down to what they consider "common sense."