Can I try them on before deciding?
'Provarli' — pro-VAR-li. The pronoun 'li' attaches to the infinitive.
Use when you have been offered replacement items and want to try before accepting. Better to check the replacement fits than to return the replacement as well.
'Provarli' is 'provare' (to try) with 'li' (them) attached as a clitic pronoun. 'Prima di + infinitive' means 'before + gerund' in English. This construction is very common in Italian: 'prima di partire' (before leaving), 'prima di mangiare' (before eating).
Posso provarla in camerino?
Can I try it on in the fitting room?
For clothing — 'la' for feminine item.
Dove sono i camerini?
Where are the fitting rooms?
Follows naturally if the answer is yes.
Posso verificare che funzioni?
Can I check that it works?
For electronics or appliances.
Italian fitting rooms ('camerini') are often staffed and have item limits. Attendants may take your items and give you a number. This is standard — not suspicious. It prevents theft and helps them track stock.