Can amox tr-k clv cure a uti?

Not first line. Augmentin (amoxicillin and clavulanate) (amoxicillin with clavulanate) is sometimes used for urinary tract infections but it's a ways down the list. Utis are typically caused by gram negative bacteria like e coli. Augmentin (amoxicillin and clavulanate) is much more effective against gram positive bugs like staph and strep.
Yes If germ is sens. Yes this antibiotic may well be effective provided the bacteria are sensitive to it. Other firstline antibiotics which urologists tend to use ahead of amox/clav are: trimethiprim/sulfa (bactrim, septra or generic), Nitrofurantoin macrocrstals (macrobid or macrodantin) or cipro (ciprofloxacin). Good luck.