Trunk problem

[dellpe]

One of my edge HP s5500 stack switches is dead, I am going to replace it with a Cisco switch Catalyst 3750 series PoE-48 via a trunk link with GE fiber port on both ends, please see the diagram below.
trunk trunk
Core switchrouter<----------S5500<--------------->Cisco Catlyst 3750

I haven’t touch Cisco switch for many years, I would like to ask the following questions:

1.) Do I need to take any precaution before connecting this Cisco switch into my HP network? Only one link between S5120 and C3750, so I don't need worry anout STP? Do I need to worry about Default vlan regarding trunking port?
2.) I need to use different trucking protocol e.g. 802.1Q etc to interconnect these two switches (S5500 and Catalyst 3750), please see the following configuration:

For S5500:

port link-type trunk
port trunk permit vlan all

Do you think the configurations above are right?

For WS-C3750X-24T-L:

switchport trunk encapsulation dot1q
switchport trunk native vlan (What you want)
switchport trunk allowed vlan (VLANs required)
switchport mode trunk
spanning-tree portfast trunk

Do I need to manually enter Duplex and speed options ?

3.)If the configurations are not right, then what are the commands for trucking port/link should I use on the Cisco switch (it uses IOS software) and HP switch? Procedures of the commands would be really helpful !
Any information and help would be much appreciated.