Lowest I've ever seen is $25.

You might be able to find lower since unusuals are uncrated all the time.

The cheapest unusual is determined by the combination of effect and model.
 
Yes. Here's a list of the worst hats by online rating.

1587 Coupe D'isaster Circling Peace Sign 1280 17 92
1588 Ol' Geezer Green Confetti 1280 27 102
1589 Bloke's Bucket Hat Green Confetti 1280 16 99
1590 Gentleman's Gatsby Green Confetti 1279 15 92
1591 Football Helmet Purple Confetti 1277 18 106
1592 Pyro's Beanie Massed Flies 1276 26 99
1593 Industrial Festivizer Massed Flies 1275 24 106
1594 Heavy Duty Rag Green Confetti 1274 21 105
1595 Buckaroos Hat Green Confetti 1274 16 93
1596 Demoman's Fro Green Confetti 1272 21 97
1597 Pyro's Beanie Green Confetti 1270 14 89
1598 Engineer's Cap Purple Confetti 1269 20 107
1599 Cadaver's Cranium Green Confetti 1267 15 101
1600 Shooter's Sola Topi Purple Confetti 1266 16 105
1601 Bombing Run Purple Confetti 1264 15 98
1602 Carouser's Capotain Green Confetti 1262 18 110
1603 Pugilist's Protector Green Confetti 1262 16 98
1604 Magnificent Mongolian Purple Confetti 1261 16 102
1605 Hard Counter Purple Confetti 1260 17 99
1606 Magnificent Mongolian Green Confetti 1259 8 82
1607 Pugilist's Protector Purple Confetti 1258 16 99
1608 Football Helmet Green Confetti 1253 17 103
1609 Madame Dixie Green Confetti 1229 12 99
1610 Coupe D'isaster Purple Confetti 1196 11 114
 
You can get a really, really shitty coupe (haha get it I made a joke, all coupes are shitty) for a buds, or about 25 refined.