Yes. Check the activity list on the home screen. If it's still pending or if it completes or goes away if it fails.
nostr:npub1mutnyacc9uc4t5mmxvpprwsauj5p2qxq95v4a9j0jxl8wnkfvuyque23vg - if I get one of those "Payment pending" warnings, do I need to keep the wallet opened?

Yes. Check the activity list on the home screen. If it's still pending or if it completes or goes away if it fails.
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