No. GTA III is single-player only.
Yes. Mods for GTA III v1.1 work fine. Avoid Steam/Definitive Edition mods. Grand Theft Auto III -3- v1.1 MULTI10 - ElAmigos
ElAmigos sometimes removes MP3s to save space. Download radio_stations.zip separately or copy from original CD. Grand Theft Auto III -3- v1.1 MULTI10 - ElAmigos