I have two questions about stp
1) I have Cisco GigaStack GBIC in mode halft-duplex. Can I enable rapid spanning-tree? Does Rapid spanning tree need link full duplex?
2) If I disable STP, Would root bridge be created? Would bpdu be exchanged between switches? How to work the switches without stp?
1-Only in full dulpex mode you should run spanning tree (PVST+)
2-Although you can turn off Spanning tree globally or per vlan, It is not recommend, because you could create layer-2 loop in the network
1) I have Cisco GigaStack GBIC in mode halft-duplex. Can I enable rapid spanning-tree? Does Rapid spanning tree need link full duplex?Won't work. GigaStacking GBIC will negotiate to 1Gb, half duplex when you connect more than 1 cable to each other. If you just connect, say, two switches using 1 GigaStacking GBIC cable the link will negotiate to full duplex. Whatever STP flavour you want, it's not worth it because the 3500XL is not that flexible. If your dealing with 2950 or 3550 then there's a possibility.
1) Rapid STP can only work between switches with a full-duplex link. You can still enable Rapid STP (rapid-pvst) on the switch, however it will only work as rapid on full-duplex links because negotiation/synchronization process is not available on half-duplex.
Please refer to the "Link Type" section in the following documentation:
2) If you disable STP on a particular switch, it will forward STP BPDU packets received from other switches on its ports in the same vlan. At the same, you should only disable STP after careful planning and consideration and if you know what issues you can encounter after disabling it.
You can read more about STP on the link below: