What part should foreign missions have in the life of the church and the individual believer?

A very prominent part. Our Lord's  last command to His disciples was:

"go ye therefore and make disciples of all nations"
Matt 28:19

It was in connection with this work that He promised His own personal fellowship. He said that when we did this: "Lo, I am with you always, even unto the end of the world."

If then the individual believer wishes to have personal fellowship with Jesus Christ, he must go into all the world and make disciples of all the nations. He may not be able to go in his own person, but in that case he can go by his gifts and by his prayers.

Any Christian who is not deeply interested in foreign missions is not in fellowship with Jesus Christ. Since a true church is a company of obedient believers, what is true of each believer will be true of the church, with the added power and blessing that issues from cooperation.

 When you support those who go out into the mission field , you are in agreement with God's heart. You are supporting and blessing “those who go and make disciples of all nations.” And because of that, you WILL receive His blessing! And your support is so urgently needed right now. I am asking you today to show your support by helping those who go out to the mission field.

I am so excited about what God is already doing through Grace World Mission, as we continue to bless them they will be able to go out on missions and make disciples of all nations. They have a wonderful heritage in the Lord and have been doing the work of the Kingdom faithfully with joy and perseverance because of your faithful gifts of the fruits of your labor that you have shared with them.

  I ask you to join me right now in a prayer of blessing on every loving heart who has responded to help meet this urgent need, and I ask that you prayerfully consider what God would have you do to help World Mission to reachout and make disciples of all nations.

 Today I’m asking you to stand up and be counted—to join the mission field of heroes down through the centuries who have done their part to deliver the Gospel message to foreign mission fields. I am asking you to make a generous, even sacrificial gift to help make it possible for others to go out to the mission field.

Your offering enables Grace World Mission, to carry on the work, on your behalf, of obedience to:

"go ye therefore and make disciples of all nations"
Matt 28:19

 http://shekinahfellowship.blogspot.com/2012/12/if-you-desire-to-donate-where-your.html