Smart cards like Icoca, Suica and Pasmo are generally valid across Japan, so don't worry about which one you buy. You can use Icoca/Pasmo/Suica for all trains, subways and buses in Osaka. You can also use Icoca/Pasmo/Suica at many shops, especially convenience stores.

Yes, you can absolutely use a Pasmo card in Osaka, as well as in most major cities across Japan. Since the nationwide integration of IC cards in 2013, the ten major transit cards—including Pasmo and Suica (from Tokyo) and Icoca (from Osaka)—have been fully interchangeable. This means you can tap your Pasmo card at ticket gates for the Osaka Metro, JR West lines, and various private railways like Hankyu, Hanshin, and Kintetsu. You can also use it to pay for city buses and at thousands of convenience stores, vending machines, and restaurants throughout the Kansai region. However, there are a few limitations: you cannot use an IC card to travel between two different regions (for example, you can't tap in at Tokyo and tap out at Osaka), and you cannot use it for the Shinkansen (bullet train) without a separate physical ticket or a specific digital registration. Additionally, while you can use and "recharge" your Pasmo at most Osaka stations, you can only get a refund for the remaining balance or return the physical card for its deposit at a station in the Tokyo area where Pasmo is issued.