Bind : MX record for send/receive mails

[Bind Users]

Hi all

I would like to know on how the MX record functioned in BIND for 
sending or receiving emails. Currently, I have a domain (eg: 
domain1.com) with MX records that used other domain's SMTP server for 
sending & receiving emails. (eg: smtp.domain2.com). 

$ORIGIN com.
domain1    IN      SOA     ns1.domain1.com. root.ns1.domain1.com. 
                          (2001082401 3600 300 604800 43200)
           IN      NS      ns1.domain1.com.
           IN      NS      ns2.domain1.com.
           IN      MX      10 smtp.domain2.com.

Questions:

1) Can it works as the smtp server is in different domain ? 
In other words, can it rely on other smtp server which is not in the 
same domain to deliver or retrieve the emails?

2) Do I have to run the smtp services on the local mail server as the 
MX record is already pointing to other smtp server in the different 
domain as the Mail Exchange ?

3) Can a user1 at domain1.com send or receive emails to user2 at domain3.com 
if the MX record for domain1.com is using smtp.domain2.com ? (Notes: 
All domains is located in different networks/geographical)

Thanz a lot in advance.